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Deck 3: Differentiation
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Question
Use implicit differentiation to find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Round your answer to 5 decimal places. 
, 
A) 0.86641
B) 0.89724
C) 0.86547
D) 1.07000
, A) 0.86641
B) 0.89724
C) 0.86547
D) 1.07000
Question
A point is moving along the graph of the function 
such that 
centimeters per second. Find 
when 
.
A)
B)
C)
D)
E)
such that centimeters per second. Find when . A)
B)
C)
D)
E)
Question
Find 
at the point 
for the equation 
.
A)
B)
C)
D)
E)
at the point for the equation . A)
B)
C)
D)
E)
Question
Find 
if 
.
A)
B)
C)
D)
E)
if . A)
B)
C)
D)
E)
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A) -257.185 ft/sec
B) -123.118 ft/sec
C) -111.364 ft/sec
D) -246.236 ft/sec
E) -235.236 ft/sec
. A silver coin is dropped from the top of a building that is 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places. A) -257.185 ft/sec
B) -123.118 ft/sec
C) -111.364 ft/sec
D) -246.236 ft/sec
E) -235.236 ft/sec
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the derivative of the function 
by the limit process.
A)
B)
C)
D)
E)
by the limit process. A)
B)
C)
D)
E)
Question
Find the derivative of the function 
by the limit process.
A)
B)
C)
D)
E)
by the limit process. A)
B)
C)
D)
E)
Question
Find the slope of the tangent line 
at the given point 
. Round your answer to two decimal places.
A) 0.67
B) 2.00
C) 1.00
D) 1.67
E) 3.00
at the given point . Round your answer to two decimal places. A) 0.67
B) 2.00
C) 1.00
D) 1.67
E) 3.00
Question
A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -16 ft per second. The position function is 
. What is the velocity of the ball after 4 seconds?
A) The velocity after 4 seconds is -80 ft per second.
B) The velocity after 4 seconds is -112 ft per second.
C) The velocity after 4 seconds is -144 ft per second.
D) The velocity after 4 seconds is -48 ft per second.
E) The velocity after 4 seconds is -288 ft per second.
. What is the velocity of the ball after 4 seconds? A) The velocity after 4 seconds is -80 ft per second.
B) The velocity after 4 seconds is -112 ft per second.
C) The velocity after 4 seconds is -144 ft per second.
D) The velocity after 4 seconds is -48 ft per second.
E) The velocity after 4 seconds is -288 ft per second.
Question
Assume that x and y are both differentiable functions of t. Find 
when 
and 
for the equation 
.
A)
B)
C)
D)
E)
when and for the equation . A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Find an equation to the tangent line to the graph of the function 
at the point 
. The coefficients below are given to two decimal places.
A)
B)
C)
D)
E)
at the point . The coefficients below are given to two decimal places. A)
B)
C)
D)
E)
Question
Use Newton's Method to approximate the zero(s) of the function 
accurate to three decimal places.
A) -0.493
B) 0.451
C) -0.546
D) 0.493
E) -0.444
accurate to three decimal places. A) -0.493
B) 0.451
C) -0.546
D) 0.493
E) -0.444
Question
Find 
in terms of x and y. 
A)
B)
C)
D)
E)
in terms of x and y. A)
B)
C)
D)
E)
Question
In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time 
. At what time will the object reach the ground level? 
A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
. At what time will the object reach the ground level? A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
Question
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Evaluate the derivative of the function at the given point. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
Question
A man 6 feet tall walks at a rate of 10 feet per second away from a light that is 15 feet above the ground (see figure). When he is 13 feet from the base of the light, at what rate is the tip of his shadow moving? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Given the derivative below find the requested higher-order derivative. 
, 
.
A)
B)
C)
D)
E)
, .
A)
B)
C)
D)
E)
Question
Apply Newton's Method to approximate the x-value of the indicated point of intersection of 
and 
. Continue the process until two successive approximations differ by less than 0.001.
and . Continue the process until two successive approximations differ by less than 0.001. Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the derivative of the trigonometric function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Use Newton's Method to approximate the zero(s) of the function 
accurate to three decimal places.
A) 0.250
B) -0.250
C) -0.292
D) 0.281
E) 0.197
accurate to three decimal places. A) 0.250
B) -0.250
C) -0.292
D) 0.281
E) 0.197
Question
Find 
in terms of x and y given that 
. Use the original equation to simplify your answer.
A)
B)
C)
D)
E)
in terms of x and y given that . Use the original equation to simplify your answer. A)
B)
C)
D)
E)
Question
Approximate the positive zero(s) of the function 
to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.
A) -1.207
B) 1.105
C) 1.082
D) -1.105
E) 1.156
to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. A) -1.207
B) 1.105
C) 1.082
D) -1.105
E) 1.156
Question
A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Differentiate the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find an equation of the tangent line to the graph of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point . A)
B)
C)
D)
E)
Question
Use the general rule to approximate 
and 
to three decimal places. 
, 
A) 1.73749, 1.61401
B) 1.65922, 1.99377
C) 1.28355, 1.44311
D) 1.56530, 1.89883
and to three decimal places. , A) 1.73749, 1.61401
B) 1.65922, 1.99377
C) 1.28355, 1.44311
D) 1.56530, 1.89883
Question
Find an equation of the line that is tangent to the graph of the function 
and parallel to the line 
.
A)
B)
C)
D)
E)
and parallel to the line . A)
B)
C)
D)
E)
Question
Evaluate the derivative of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point . A)
B)
C)
D)
E)
Question
Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27 in 2006 is approximated by the model 
, 
where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand. 
A) 15.7; 23.8
B) 18.2; 21.6
C) 16.7; 22.8
D) 15.7; 22.8
E) 16.7; 21.6
, where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand. A) 15.7; 23.8
B) 18.2; 21.6
C) 16.7; 22.8
D) 15.7; 22.8
E) 16.7; 21.6
Question
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
A)
and 
B)
C)
and 
D)
E) The graph has no horizontal tangents.
A)
and B)
C)
and D)
E) The graph has no horizontal tangents.
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Suppose that an automobile's velocity starting from rest is 
where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place.
A) 1.1 ft/sec2
B) 1.8 ft/sec2
C) 1.0 ft/sec2
D) 0.2 ft/sec2
E) 12.4 ft/sec2
where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place. A) 1.1 ft/sec2
B) 1.8 ft/sec2
C) 1.0 ft/sec2
D) 0.2 ft/sec2
E) 12.4 ft/sec2
Question
The graph of the function f is given below. Select the graph of 
. 
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
Question
Use logarithmic differentiation to find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find 
by implicit differentiation. 
A)
B)
C)
D)
E)
by implicit differentiation. A)
B)
C)
D)
E)
Question
Suppose a 20-centimeter pendulum moves according to the equation 
where 
is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of 
when 
seconds. Round your answer to four decimal places.
A) 1.669 radians per second
B) 2.7841 radians per second
C) 0.3815 radians per second
D) 1.8396 radians per second
E) 6.6763 radians per second
where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places. A) 1.669 radians per second
B) 2.7841 radians per second
C) 0.3815 radians per second
D) 1.8396 radians per second
E) 6.6763 radians per second
Question
Find 
by implicit differentiation. 
A)
B)
C)
D)
E)
by implicit differentiation. A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
at 
A)
B)
C)
D)
E)
at A)
B)
C)
D)
E)
Question
Find the derivative of the function 
. Simplify your answer.
A)
B)
C)
D)
E)
. Simplify your answer. A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Use logarithmic differentiation to find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Find 
if 
.
A)
B)
C)
D)
E)
if . A)
B)
C)
D)
E)
Question
The ordering and transportation cost C for the components used in manufacturing a product is 
, 
where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for 
. Round your answer to two decimal places.
A) -6.20 thousand dollars per hundred
B) 7.41 thousand dollars per hundred
C) 3.13 thousand dollars per hundred
D) -5.03 thousand dollars per hundred
E) -8.02 thousand dollars per hundred
, where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for . Round your answer to two decimal places. A) -6.20 thousand dollars per hundred
B) 7.41 thousand dollars per hundred
C) 3.13 thousand dollars per hundred
D) -5.03 thousand dollars per hundred
E) -8.02 thousand dollars per hundred
Question
Use the rules of differentiation to find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
A buoy oscillates in simple harmonic motion 
as waves move past it. The buoy moves a total of 
feet (vertically) between its low point and its high point. It returns to its high point every 
seconds. Determine the velocity of the buoy as a function of t.
A)
B)
C)
D)
E)
as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t. A)
B)
C)
D)
E)
Question
All edges of a cube are expanding at a rate of 7 centimeters per second. How fast is the volume changing when each edge is 2 centimeters?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
An airplane is flying in still air with an airspeed of 283 miles per hour. If it is climbing at an angle of 21°, find the rate at which it is gaining altitude. Round your answer to four decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time 
. Find the rate of change of the angle of elevation of the camera when 
. Round your answer to four decimal places. 
A)
B)
C)
D)
E)
. Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places. A)
B)
C)
D)
E)
Question
Find 
by implicit differentiation. 
.
A)
B)
C)
D)
E)
by implicit differentiation. .
A)
B)
C)
D)
E)
Question
A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write 
as a function of x. 
A)
B)
C)
D)
E)
as a function of x. A)
B)
C)
D)
E)
Question
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
C)
and 
D)
and 
E) The graph has no horizontal tangents.
A)
B)
C)
and D)
and E) The graph has no horizontal tangents.
Question
Find the rate of change of the distance D between the origin and a moving point on the graph of 
if 
centimeters per second.
A)
B)
C)
D)
E)
if centimeters per second. A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Use the alternative form of the derivative to find the derivative of the function 
at 
.
A)
B)
C)
D)
E)
at . A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Use implicit differentiation to find an equation of the tangent line to the ellipse 
at 
.
A)
B)
C)
D)
E)
at . A)
B)
C)
D)
E)
Question
Find the slope-intercept equation of the line tangent to the graph of 
when 
.
A)
B)
C)
D)
E)
when . A)
B)
C)
D)
E)
Question
Find the derivative of the algebraic function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find an equation of the tangent line to the graph of f at the given point. 
, at 
A)
B)
C)
D)
E)
, at A)
B)
C)
D)
E)
Question
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find 
by implicit differentiation. 
A)
B)
C)
D)
E)
by implicit differentiation. A)
B)
C)
D)
E)
Question
A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of 
with the perpendicular from the light to the wall. 
A)
B)
C)
D)
E)
with the perpendicular from the light to the wall. A)
B)
C)
D)
E)
Question
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
and 
C)
and 
D)
E) The graph has no horizontal tangents.
A)
B)
and C)
and D)
E) The graph has no horizontal tangents.
Question
A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is 
.
What is its velocity after 3 seconds?
A) The velocity after 3 seconds is 229.3 meters per second.
B) The velocity after 3 seconds is -136.7 meters per second.
C) The velocity after 3 seconds is 92.6 meters per second.
D) The velocity after 3 seconds is 107.3 meters per second.
E) The velocity after 3 seconds is -151.4 meters per second
. What is its velocity after 3 seconds?
A) The velocity after 3 seconds is 229.3 meters per second.
B) The velocity after 3 seconds is -136.7 meters per second.
C) The velocity after 3 seconds is 92.6 meters per second.
D) The velocity after 3 seconds is 107.3 meters per second.
E) The velocity after 3 seconds is -151.4 meters per second
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when 
.
A) -130 ft/sec
B) -34 ft/sec
C) -21 ft/sec
D) -195 ft/sec
E) -65 ft/sec
. A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when . A) -130 ft/sec
B) -34 ft/sec
C) -21 ft/sec
D) -195 ft/sec
E) -65 ft/sec
Question
Complete two iterations of Newton's Method to approximate a zero of the function using the given initial guess. What is the value of 
of such an approximation? Round your answer to 5 decimal places. 
, 
A) 85.42370
B) 78.37037
C) 86.20741
D) 86.99111
of such an approximation? Round your answer to 5 decimal places. , A) 85.42370
B) 78.37037
C) 86.20741
D) 86.99111
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the points at which the graph of the equation has a vertical or horizontal tangent line. 
A) There is a vertical tangent at
but no horizontal tangents.
B) There is a horizontal tangent at
and a vertical tangent at 
.
C) There is a horizontal tangent at
but no vertical tangents.
D) There is a horizontal tangent at
and a vertical tangent at 
.
E) There are no horizontal or vertical tangent lines.
A) There is a vertical tangent at
but no horizontal tangents.B) There is a horizontal tangent at
and a vertical tangent at .C) There is a horizontal tangent at
but no vertical tangents.D) There is a horizontal tangent at
and a vertical tangent at .E) There are no horizontal or vertical tangent lines.
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
if 
.
A)
B)
C)
D)
E)
if . A)
B)
C)
D)
E)
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Deck 3: Differentiation
1
Use implicit differentiation to find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
A
2
Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Round your answer to 5 decimal places. ,
A) 0.86641
B) 0.89724
C) 0.86547
D) 1.07000
, A) 0.86641
B) 0.89724
C) 0.86547
D) 1.07000
C
3
A point is moving along the graph of the function such that centimeters per second. Find when .
A)
B)
C)
D)
E)
such that centimeters per second. Find when . A)
B)
C)
D)
E)
E
4
Find at the point for the equation .
A)
B)
C)
D)
E)
at the point for the equation . A)
B)
C)
D)
E)
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5
Find if .
A)
B)
C)
D)
E)
if . A)
B)
C)
D)
E)
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6
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A) -257.185 ft/sec
B) -123.118 ft/sec
C) -111.364 ft/sec
D) -246.236 ft/sec
E) -235.236 ft/sec
. A silver coin is dropped from the top of a building that is 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places. A) -257.185 ft/sec
B) -123.118 ft/sec
C) -111.364 ft/sec
D) -246.236 ft/sec
E) -235.236 ft/sec
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7
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
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8
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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9
Find the derivative of the function by the limit process.
A)
B)
C)
D)
E)
by the limit process. A)
B)
C)
D)
E)
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10
Find the derivative of the function by the limit process.
A)
B)
C)
D)
E)
by the limit process. A)
B)
C)
D)
E)
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11
Find the slope of the tangent line at the given point . Round your answer to two decimal places.
A) 0.67
B) 2.00
C) 1.00
D) 1.67
E) 3.00
at the given point . Round your answer to two decimal places. A) 0.67
B) 2.00
C) 1.00
D) 1.67
E) 3.00
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12
A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -16 ft per second. The position function is . What is the velocity of the ball after 4 seconds?
A) The velocity after 4 seconds is -80 ft per second.
B) The velocity after 4 seconds is -112 ft per second.
C) The velocity after 4 seconds is -144 ft per second.
D) The velocity after 4 seconds is -48 ft per second.
E) The velocity after 4 seconds is -288 ft per second.
. What is the velocity of the ball after 4 seconds? A) The velocity after 4 seconds is -80 ft per second.
B) The velocity after 4 seconds is -112 ft per second.
C) The velocity after 4 seconds is -144 ft per second.
D) The velocity after 4 seconds is -48 ft per second.
E) The velocity after 4 seconds is -288 ft per second.
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13
Assume that x and y are both differentiable functions of t. Find when and for the equation .
A)
B)
C)
D)
E)
when and for the equation . A)
B)
C)
D)
E)
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14
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
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15
Find an equation to the tangent line to the graph of the function at the point . The coefficients below are given to two decimal places.
A)
B)
C)
D)
E)
at the point . The coefficients below are given to two decimal places. A)
B)
C)
D)
E)
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16
Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places.
A) -0.493
B) 0.451
C) -0.546
D) 0.493
E) -0.444
accurate to three decimal places. A) -0.493
B) 0.451
C) -0.546
D) 0.493
E) -0.444
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17
Find in terms of x and y.
A)
B)
C)
D)
E)
in terms of x and y. A)
B)
C)
D)
E)
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18
In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level?
A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
. At what time will the object reach the ground level? A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
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19
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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20
Evaluate the derivative of the function at the given point. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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21
A man 6 feet tall walks at a rate of 10 feet per second away from a light that is 15 feet above the ground (see figure). When he is 13 feet from the base of the light, at what rate is the tip of his shadow moving?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
Given the derivative below find the requested higher-order derivative. , .
A)
B)
C)
D)
E)
, .
A)
B)
C)
D)
E)
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23
Apply Newton's Method to approximate the x-value of the indicated point of intersection of and . Continue the process until two successive approximations differ by less than 0.001.
and . Continue the process until two successive approximations differ by less than 0.001. Unlock Deck
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24
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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25
Find the derivative of the trigonometric function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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26
Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places.
A) 0.250
B) -0.250
C) -0.292
D) 0.281
E) 0.197
accurate to three decimal places. A) 0.250
B) -0.250
C) -0.292
D) 0.281
E) 0.197
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27
Find in terms of x and y given that . Use the original equation to simplify your answer.
A)
B)
C)
D)
E)
in terms of x and y given that . Use the original equation to simplify your answer. A)
B)
C)
D)
E)
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28
Approximate the positive zero(s) of the function to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.
A) -1.207
B) 1.105
C) 1.082
D) -1.105
E) 1.156
to three decimal places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. A) -1.207
B) 1.105
C) 1.082
D) -1.105
E) 1.156
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29
A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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31
Differentiate the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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32
Find an equation of the tangent line to the graph of the function at the point .
A)
B)
C)
D)
E)
at the point . A)
B)
C)
D)
E)
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33
Use the general rule to approximate and to three decimal places. ,
A) 1.73749, 1.61401
B) 1.65922, 1.99377
C) 1.28355, 1.44311
D) 1.56530, 1.89883
and to three decimal places. , A) 1.73749, 1.61401
B) 1.65922, 1.99377
C) 1.28355, 1.44311
D) 1.56530, 1.89883
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34
Find an equation of the line that is tangent to the graph of the function and parallel to the line .
A)
B)
C)
D)
E)
and parallel to the line . A)
B)
C)
D)
E)
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35
Evaluate the derivative of the function at the point .
A)
B)
C)
D)
E)
at the point . A)
B)
C)
D)
E)
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36
Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27 in 2006 is approximated by the model , where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand.
A) 15.7; 23.8
B) 18.2; 21.6
C) 16.7; 22.8
D) 15.7; 22.8
E) 16.7; 21.6
, where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand. A) 15.7; 23.8
B) 18.2; 21.6
C) 16.7; 22.8
D) 15.7; 22.8
E) 16.7; 21.6
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37
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
A) and
B)
C) and
D)
E) The graph has no horizontal tangents.
A)
and B)
C)
and D)
E) The graph has no horizontal tangents.
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38
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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39
Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place.
A) 1.1 ft/sec2
B) 1.8 ft/sec2
C) 1.0 ft/sec2
D) 0.2 ft/sec2
E) 12.4 ft/sec2
where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place. A) 1.1 ft/sec2
B) 1.8 ft/sec2
C) 1.0 ft/sec2
D) 0.2 ft/sec2
E) 12.4 ft/sec2
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40
The graph of the function f is given below. Select the graph of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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41
Use logarithmic differentiation to find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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42
Find by implicit differentiation.
A)
B)
C)
D)
E)
by implicit differentiation. A)
B)
C)
D)
E)
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43
Suppose a 20-centimeter pendulum moves according to the equation where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places.
A) 1.669 radians per second
B) 2.7841 radians per second
C) 0.3815 radians per second
D) 1.8396 radians per second
E) 6.6763 radians per second
where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places. A) 1.669 radians per second
B) 2.7841 radians per second
C) 0.3815 radians per second
D) 1.8396 radians per second
E) 6.6763 radians per second
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44
Find by implicit differentiation.
A)
B)
C)
D)
E)
by implicit differentiation. A)
B)
C)
D)
E)
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45
Find the slope of the graph of the function at the given value. at
A)
B)
C)
D)
E)
at A)
B)
C)
D)
E)
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46
Find the derivative of the function . Simplify your answer.
A)
B)
C)
D)
E)
. Simplify your answer. A)
B)
C)
D)
E)
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47
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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48
Use logarithmic differentiation to find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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49
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
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50
Find if .
A)
B)
C)
D)
E)
if . A)
B)
C)
D)
E)
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51
The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for . Round your answer to two decimal places.
A) -6.20 thousand dollars per hundred
B) 7.41 thousand dollars per hundred
C) 3.13 thousand dollars per hundred
D) -5.03 thousand dollars per hundred
E) -8.02 thousand dollars per hundred
, where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for . Round your answer to two decimal places. A) -6.20 thousand dollars per hundred
B) 7.41 thousand dollars per hundred
C) 3.13 thousand dollars per hundred
D) -5.03 thousand dollars per hundred
E) -8.02 thousand dollars per hundred
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52
Use the rules of differentiation to find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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53
A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t.
A)
B)
C)
D)
E)
as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t. A)
B)
C)
D)
E)
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54
All edges of a cube are expanding at a rate of 7 centimeters per second. How fast is the volume changing when each edge is 2 centimeters?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
An airplane is flying in still air with an airspeed of 283 miles per hour. If it is climbing at an angle of 21°, find the rate at which it is gaining altitude. Round your answer to four decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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57
In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places.
A)
B)
C)
D)
E)
. Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places. A)
B)
C)
D)
E)
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58
Find by implicit differentiation. .
A)
B)
C)
D)
E)
by implicit differentiation. .
A)
B)
C)
D)
E)
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59
A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write as a function of x.
A)
B)
C)
D)
E)
as a function of x. A)
B)
C)
D)
E)
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60
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
A)
B)
C) and
D) and
E) The graph has no horizontal tangents.
A)
B)
C)
and D)
and E) The graph has no horizontal tangents.
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61
Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.
A)
B)
C)
D)
E)
if centimeters per second. A)
B)
C)
D)
E)
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62
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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63
Use the alternative form of the derivative to find the derivative of the function at .
A)
B)
C)
D)
E)
at . A)
B)
C)
D)
E)
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64
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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65
Use implicit differentiation to find an equation of the tangent line to the ellipse at .
A)
B)
C)
D)
E)
at . A)
B)
C)
D)
E)
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66
Find the slope-intercept equation of the line tangent to the graph of when .
A)
B)
C)
D)
E)
when . A)
B)
C)
D)
E)
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67
Find the derivative of the algebraic function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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68
Find an equation of the tangent line to the graph of f at the given point. , at
A)
B)
C)
D)
E)
, at A)
B)
C)
D)
E)
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69
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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70
Find by implicit differentiation.
A)
B)
C)
D)
E)
by implicit differentiation. A)
B)
C)
D)
E)
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71
A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.
A)
B)
C)
D)
E)
with the perpendicular from the light to the wall. A)
B)
C)
D)
E)
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72
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
A)
B) and
C) and
D)
E) The graph has no horizontal tangents.
A)
B)
and C)
and D)
E) The graph has no horizontal tangents.
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73
A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is .
What is its velocity after 3 seconds?
A) The velocity after 3 seconds is 229.3 meters per second.
B) The velocity after 3 seconds is -136.7 meters per second.
C) The velocity after 3 seconds is 92.6 meters per second.
D) The velocity after 3 seconds is 107.3 meters per second.
E) The velocity after 3 seconds is -151.4 meters per second
. What is its velocity after 3 seconds?
A) The velocity after 3 seconds is 229.3 meters per second.
B) The velocity after 3 seconds is -136.7 meters per second.
C) The velocity after 3 seconds is 92.6 meters per second.
D) The velocity after 3 seconds is 107.3 meters per second.
E) The velocity after 3 seconds is -151.4 meters per second
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74
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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75
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when .
A) -130 ft/sec
B) -34 ft/sec
C) -21 ft/sec
D) -195 ft/sec
E) -65 ft/sec
. A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when . A) -130 ft/sec
B) -34 ft/sec
C) -21 ft/sec
D) -195 ft/sec
E) -65 ft/sec
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76
Complete two iterations of Newton's Method to approximate a zero of the function using the given initial guess. What is the value of of such an approximation? Round your answer to 5 decimal places. ,
A) 85.42370
B) 78.37037
C) 86.20741
D) 86.99111
of such an approximation? Round your answer to 5 decimal places. , A) 85.42370
B) 78.37037
C) 86.20741
D) 86.99111
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77
Find the derivative of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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78
Find the points at which the graph of the equation has a vertical or horizontal tangent line.
A) There is a vertical tangent at but no horizontal tangents.
B) There is a horizontal tangent at and a vertical tangent at .
C) There is a horizontal tangent at but no vertical tangents.
D) There is a horizontal tangent at and a vertical tangent at .
E) There are no horizontal or vertical tangent lines.
A) There is a vertical tangent at
but no horizontal tangents.B) There is a horizontal tangent at
and a vertical tangent at .C) There is a horizontal tangent at
but no vertical tangents.D) There is a horizontal tangent at
and a vertical tangent at .E) There are no horizontal or vertical tangent lines.
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79
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 193 flashcards in this deck.
Unlock Deck
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80
Find if .
A)
B)
C)
D)
E)
if . A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 193 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 193 flashcards in this deck.
