Question 1

Find the domain of the function. $$f ( x ) = \sqrt { 49 - x ^ { 2 } }$$

Accepted Answer

The answer of Find the domain of the function. \[f...

Question 2

The graph shown gives the weight of a certain person as a function of age.Find the age at which the person started an exercise program.

Accepted Answer

A) 20 
B) 54 
C) 38 
D) 30 
E) 35 
A) 20 
B) 54 
C) 38 
D) 30 
E) 35

Question 3

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. 
$y = 4 + 2 x - x ^ { 2 }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

$$\text { Write an equation that expresses the fact that a function } f \text { is continuous at the number } 4 \text {. }$$

Accepted Answer

The answer of \[\text { Write an equation that expresses...

Question 5

$$\text { Let } f ( x ) = x ^ { 2 } - 18 x + 75 \text { and } g ( x ) = \sqrt { x + 7 } \text {. Find } ( f \circ g ) ( 74 ) ( g \circ g ) ( 74 ) \text {. }$$

Accepted Answer

The answer of \[\text { Let } f ( x...

Question 6

Find the domain of the function $f ( x ) = \frac { x } { - 2 \sin x - 3 }$.

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left[ - \frac { 3 } { 2 } , \infty \right)$ 
C)  $[ - 3 , - 2 ]$ 
D)  $[ 2,3 ]$ 
A)  $( - \infty , \infty )$ 
B)  $\left[ - \frac { 3 } { 2 } , \infty \right)$ 
C)  $[ - 3 , - 2 ]$ 
D)  $[ 2,3 ]$

Question 7

Evaluate the limit. $$\lim _ { x \rightarrow 3 } \left( \frac { x ^ { 3 } - 5 } { x ^ { 2 } - 6 } \right)$$

Accepted Answer

The answer of Evaluate the limit. \[\lim _ { x...

Question 8

Determine whether the function whose graph is given is even, odd, or neither.

Accepted Answer

The answer of Determine whether the function whose graph is...

Question 9

$$\text { Find the limit } \lim _ { x \rightarrow 0 ^ { + } } \frac { 9 + \sqrt { x } } { \sqrt { x + 16 } } \text {. }$$

Accepted Answer

The answer of \[\text { Find the limit } \lim...

Question 10

$$\text { If } f \text { and } g \text { are continuous functions with } f ( 9 ) = 6 \text { and } \lim _ { x \rightarrow 9 } [ 2 f ( x ) - g ( x ) ] = 9 \text {, find } g ( 9 ) \text {. }$$

Accepted Answer

The answer of \[\text { If } f \text {...

Question 11

If the point $( 7,3 )$ is on the graph of an even function, what other point must also be on the graph? Select the correct answer.

Accepted Answer

A)  $( - 7 , - 3 )$ 
B)  $( 7 , - 3 )$ 
C)  $( 0,0 )$ 
D)  $( - 7,3 )$ 
E)  None of these 
A)  $( - 7 , - 3 )$ 
B)  $( 7 , - 3 )$ 
C)  $( 0,0 )$ 
D)  $( - 7,3 )$ 
E)  None of these

Question 12

It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species $S$ of bats living in caves in central Mexico has been related to the surface area $A$ measured in $m ^ { 2 }$ of the caves by the equation $S = 0.7 A ^ { 03 }$
(a) The cave called mission impossible near puebla, mexico, has suface area of $A = 90 \mathrm {~m} ^ { 2 }$. How many species of bats would expect to find in that cave?
(b) If you discover that 5 species of bats live in cave estimate the area of the cave.

Accepted Answer

a) 3 speci

Question 13

A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after $t$ minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with $t = 38$ and $t = 42$.
$\begin{array}{|c|c|c|c|c|c|}
\hline t \text { (mins) } & 36 & 38 & 40 & 42 & 44 \
\hline \text { Heartbeats } & 2570 & 2720 & 2840 & 3020 & 3070 \
\hline
\end{array}$

Select the correct answer.

Accepted Answer

A)  74 
B)  80 
C)  85 
D)  70 
E)  76
F) 75 
A)  74 
B)  80 
C)  85 
D)  70 
E)  76
F) 75

Question 14

$\text { Find the limit } \lim _ { x \rightarrow 5 } \frac { x + 1 } { x ^ { 2 } - 4 x + 2 } \text {. }$

Accepted Answer

The answer of \(\text { Find the limit } \lim...

Question 15

Find the limit. $\lim _ { x \rightarrow - \infty } \frac { \sqrt { x ^ { 2 } - 25 } } { 2 x - 6 }$

Accepted Answer

The answer of Find the limit. \(\lim _ { x...

Question 16

Define the function $f ( x ) = \frac { 6 x ^ { 3 } + x } { 4 x }$ at 0 so as to make it continuous at 0 .

Accepted Answer

A)  $f ( 0 ) = \frac { 3 } { 2 }$ 
B)  $f ( 0 ) = \frac { 7 } { 4 }$ 
C)  $f ( 0 ) = 0$ 
D)  $f ( 0 ) = \frac { 1 } { 4 }$ 
A)  $f ( 0 ) = \frac { 3 } { 2 }$ 
B)  $f ( 0 ) = \frac { 7 } { 4 }$ 
C)  $f ( 0 ) = 0$ 
D)  $f ( 0 ) = \frac { 1 } { 4 }$

Question 17

Is there a number $a$ such that $\lim _ { x \rightarrow - 3 } \frac { 3 x ^ { 2 } + a x + a + 3 } { x ^ { 2 } + x - 6 }$ exists? If so, find the value of $a$ and the value of the limit.

Accepted Answer

a= 15, lim

Question 18

Use the graph to determine where the function is discontinuous.

Accepted Answer

The answer of Use the graph to determine where the...

Question 19

Find the limit. $$\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }$$

Accepted Answer

A)  6 
B)  10 
C)  12
D 1 
A)  6 
B)  10 
C)  12
D 1

Question 20

Find $a$, such that the function $f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }$ has the domain $( - 4,4 )$.
Select the correct answer.

Accepted Answer

A)  $a = - 16$ 
B)  $a = \sqrt { 4 }$ 
C)  $a = - \sqrt { 4 }$ 
D)  $a = 16$ 
E)  $a = 4$ 
A)  $a = - 16$ 
B)  $a = \sqrt { 4 }$ 
C)  $a = - \sqrt { 4 }$ 
D)  $a = 16$ 
E)  $a = 4$

Find the domain of the function. $f ( x ) = \sqrt { 49 - x ^ { 2 } }$

The graph shown gives the weight of a certain person as a function of age.Find the age at which the person started an exercise program.

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. $y = 4 + 2 x - x ^ { 2 }$

$\text { Write an equation that expresses the fact that a function } f \text { is continuous at the number } 4 \text {. }$

$\text { Let } f ( x ) = x ^ { 2 } - 18 x + 75 \text { and } g ( x ) = \sqrt { x + 7 } \text {. Find } ( f \circ g ) ( 74 ) ( g \circ g ) ( 74 ) \text {. }$

Find the domain of the function $f ( x ) = \frac { x } { - 2 \sin x - 3 }$ .

Evaluate the limit. $\lim _ { x \rightarrow 3 } \left( \frac { x ^ { 3 } - 5 } { x ^ { 2 } - 6 } \right)$

Determine whether the function whose graph is given is even, odd, or neither.

$\text { Find the limit } \lim _ { x \rightarrow 0 ^ { + } } \frac { 9 + \sqrt { x } } { \sqrt { x + 16 } } \text {. }$

$\text { If } f \text { and } g \text { are continuous functions with } f ( 9 ) = 6 \text { and } \lim _ { x \rightarrow 9 } [ 2 f ( x ) - g ( x ) ] = 9 \text {, find } g ( 9 ) \text {. }$

If the point $( 7,3 )$ is on the graph of an even function, what other point must also be on the graph? Select the correct answer.

$\text { Find the limit } \lim _ { x \rightarrow 5 } \frac { x + 1 } { x ^ { 2 } - 4 x + 2 } \text {. }$

Find the limit. $\lim _ { x \rightarrow - \infty } \frac { \sqrt { x ^ { 2 } - 25 } } { 2 x - 6 }$

Define the function $f ( x ) = \frac { 6 x ^ { 3 } + x } { 4 x }$ at 0 so as to make it continuous at 0 .

Is there a number $a$ such that $\lim _ { x \rightarrow - 3 } \frac { 3 x ^ { 2 } + a x + a + 3 } { x ^ { 2 } + x - 6 }$ exists? If so, find the value of $a$ and the value of the limit.

Use the graph to determine where the function is discontinuous.

Find the limit. $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }$

Find $a$ , such that the function $f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }$ has the domain $( - 4,4 )$ . Select the correct answer.

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 1: Functions and Models

Find the domain of the function. f(x)=49−x2f ( x ) = \sqrt { 49 - x ^ { 2 } }f(x)=49−x2​

The graph shown gives the weight of a certain person as a function of age.Find the age at which the person started an exercise program.

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. y=4+2x−x2y = 4 + 2 x - x ^ { 2 }y=4+2x−x2

Let f(x)=x2−18x+75 and g(x)=x+7. Find (f∘g)(74)(g∘g)(74). \text { Let } f ( x ) = x ^ { 2 } - 18 x + 75 \text { and } g ( x ) = \sqrt { x + 7 } \text {. Find } ( f \circ g ) ( 74 ) ( g \circ g ) ( 74 ) \text {. } Let f(x)=x2−18x+75 and g(x)=x+7​. Find (f∘g)(74)(g∘g)(74).

Find the domain of the function f(x)=x−2sin⁡x−3f ( x ) = \frac { x } { - 2 \sin x - 3 }f(x)=−2sinx−3x​ .

Evaluate the limit. lim⁡x→3(x3−5x2−6)\lim _ { x \rightarrow 3 } \left( \frac { x ^ { 3 } - 5 } { x ^ { 2 } - 6 } \right)limx→3​(x2−6x3−5​)

Determine whether the function whose graph is given is even, odd, or neither.

Find the limit lim⁡x→0+9+xx+16. \text { Find the limit } \lim _ { x \rightarrow 0 ^ { + } } \frac { 9 + \sqrt { x } } { \sqrt { x + 16 } } \text {. } Find the limit limx→0+​x+16​9+x​​.

If the point (7,3)( 7,3 )(7,3) is on the graph of an even function, what other point must also be on the graph? Select the correct answer.

Find the limit lim⁡x→5x+1x2−4x+2. \text { Find the limit } \lim _ { x \rightarrow 5 } \frac { x + 1 } { x ^ { 2 } - 4 x + 2 } \text {. } Find the limit limx→5​x2−4x+2x+1​.

Find the limit. lim⁡x→−∞x2−252x−6\lim _ { x \rightarrow - \infty } \frac { \sqrt { x ^ { 2 } - 25 } } { 2 x - 6 }limx→−∞​2x−6x2−25​​

Define the function f(x)=6x3+x4xf ( x ) = \frac { 6 x ^ { 3 } + x } { 4 x }f(x)=4x6x3+x​ at 0 so as to make it continuous at 0 .

Is there a number aaa such that lim⁡x→−33x2+ax+a+3x2+x−6\lim _ { x \rightarrow - 3 } \frac { 3 x ^ { 2 } + a x + a + 3 } { x ^ { 2 } + x - 6 }limx→−3​x2+x−63x2+ax+a+3​ exists? If so, find the value of aaa and the value of the limit.

Use the graph to determine where the function is discontinuous.

Find the limit. lim⁡x→2x2+2x−12x−2\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }limx→2​x−2x2+2x−12​

Find aaa , such that the function f(x)=4x+a−x2f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }f(x)=4x+a−x2​ has the domain (−4,4)( - 4,4 )(−4,4) . Select the correct answer.

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Find the domain of the function. $f ( x ) = \sqrt { 49 - x ^ { 2 } }$

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. $y = 4 + 2 x - x ^ { 2 }$

$\text { Let } f ( x ) = x ^ { 2 } - 18 x + 75 \text { and } g ( x ) = \sqrt { x + 7 } \text {. Find } ( f \circ g ) ( 74 ) ( g \circ g ) ( 74 ) \text {. }$

Find the domain of the function $f ( x ) = \frac { x } { - 2 \sin x - 3 }$ .

Evaluate the limit. $\lim _ { x \rightarrow 3 } \left( \frac { x ^ { 3 } - 5 } { x ^ { 2 } - 6 } \right)$

$\text { Find the limit } \lim _ { x \rightarrow 0 ^ { + } } \frac { 9 + \sqrt { x } } { \sqrt { x + 16 } } \text {. }$

If the point $( 7,3 )$ is on the graph of an even function, what other point must also be on the graph? Select the correct answer.

$\text { Find the limit } \lim _ { x \rightarrow 5 } \frac { x + 1 } { x ^ { 2 } - 4 x + 2 } \text {. }$

Find the limit. $\lim _ { x \rightarrow - \infty } \frac { \sqrt { x ^ { 2 } - 25 } } { 2 x - 6 }$

Define the function $f ( x ) = \frac { 6 x ^ { 3 } + x } { 4 x }$ at 0 so as to make it continuous at 0 .

Is there a number $a$ such that $\lim _ { x \rightarrow - 3 } \frac { 3 x ^ { 2 } + a x + a + 3 } { x ^ { 2 } + x - 6 }$ exists? If so, find the value of $a$ and the value of the limit.

Find the limit. $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }$

Find $a$ , such that the function $f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }$ has the domain $( - 4,4 )$ . Select the correct answer.