Question 1

Express the integral as a limit of sums.Then evaluate the limit.

Accepted Answer

The answer of Express the integral as a limit of...

Question 2

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

Accepted Answer

A)  	0.6 miles
B)  	0.8 miles
C)  	2.4 miles
D)  	1.8 miles
E)  	1.2 miles E

Question 3

Find a function  such that  for x > 0 and some number a.

Accepted Answer

; for

Question 4

Evaluate the indefinite integral.

Accepted Answer

The answer of Evaluate the indefinite integral. ...

Question 5

The velocity graph of a car accelerating from rest to a speed of 7 km/h over a period of 10 seconds is shown.Estimate to the nearest integer the distance traveled during this period.Use a right sum with n = 10.

Accepted Answer

The answer of The velocity graph of a car accelerating...

Question 6

Evaluate the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 7

Evaluate the integral by making the given substitution.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

By reading values from the given graph of f ,use five rectangles to find a lower estimate,to the nearest whole number,for the area from 0 to 10 under the given graph of f.

Accepted Answer

The answer of By reading values from the given graph...

Question 9

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)   none of these

Question 10

The area of the region that lies to the right of the y-axis and to the left of the parabola  (the shaded region in the figure)is given by the integral  . Find the area..

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Evaluate by interpreting it in terms of

Accepted Answer

The answer of Evaluate by interpreting it in terms of...

Question 12

The acceleration function (in m/  )and the initial velocity are given for a particle moving along a line.Find the velocity at time t and the distance traveled during the given time interval.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Given that  ,find  .

Accepted Answer

The answer of Given that  ,find  ....

Question 14

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. ...

Question 15

The velocity graph of a braking car is shown.Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied.Use a left sum with n = 7.

Accepted Answer

The answer of The velocity graph of a braking car...

Question 16

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Use the Midpoint Rule with n = 10 to approximate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

A table of values of an increasing function f(x) is shown.Use the table to find an upper estimate of

Accepted Answer

The answer of A table of values of an increasing...

Question 19

Use the Midpoint Rule with n = 5 to approximate the integral.  Round your answer to three decimal places.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Find the average value of the function on the given interval.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 4: Applications of Differentiation

Express the integral as a limit of sums.Then evaluate the limit.

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

Find a function such that for x > 0 and some number a.

Evaluate the indefinite integral.

The velocity graph of a car accelerating from rest to a speed of 7 km/h over a period of 10 seconds is shown.Estimate to the nearest integer the distance traveled during this period.Use a right sum with n = 10.

Evaluate the indefinite integral.

Evaluate the integral by making the given substitution.

By reading values from the given graph of f ,use five rectangles to find a lower estimate,to the nearest whole number,for the area from 0 to 10 under the given graph of f.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral . Find the area..

Evaluate by interpreting it in terms of areas

The acceleration function (in m/ ) and the initial velocity are given for a particle moving along a line.Find the velocity at time t and the distance traveled during the given time interval.

Given that ,find .

Evaluate the definite integral.

The velocity graph of a braking car is shown.Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied.Use a left sum with n = 7.

Evaluate the integral.

Use the Midpoint Rule with n = 10 to approximate the integral.

A table of values of an increasing function f(x) is shown.Use the table to find an upper estimate of

Use the Midpoint Rule with n = 5 to approximate the integral. Round your answer to three decimal places.

Find the average value of the function on the given interval.