Deck 4: Applications of Differentiation

Question 1

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.

A)
B)
C)
D)
E)

Answer 1

Question 2

Evaluate the integral.

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B)
C)
D)
E)

Answer 2

Question 3

Evaluate the integral.

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B)
C)
D)
E)

Answer 3

Question 4

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

Question 5

The velocity function (in meters per second)is given for a particle moving along a line.Find the distance traveled by the particle during the given time interval.

A) 68 m
B) 100 m
C) 64 m
D) 36 m
E) 72 m

Question 6

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

A)
B)
C)
D)
E)

Question 7

Evaluate the indefinite integral.

Question 8

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.

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

Question 9

If and ,find .

A)
B)
C)
D)
E)

Question 10

Evaluate the integral by making the given substitution.

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B)
C)
D)
E)

Question 11

Evaluate the definite integral.

Question 12

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..

A)
B)
C)
D)
E)

Question 13

Evaluate the indefinite integral.

A)
B)
C)
D)

Question 14

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

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B)
C)
D)
E)

Question 15

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

Question 16

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

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

Question 17

Evaluate the integral.

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B)
C)
D)
E)

Question 18

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

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B)
C)
D)
E)

Question 19

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

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B)
C)
D)
E)

Question 20

Evaluate the Riemann sum for with four subintervals,taking the sample points to be right endpoints.

A)
B)
C)
D)
E)

Question 21

Evaluate by interpreting it in terms of areas

Question 22

Evaluate by interpreting it in terms of areas.

Question 23

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.

Question 24

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

Question 25

Determine a region whose area is equal to .

A)
B)
C)
D)
E)

Question 26

Given that ,find .

Question 27

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.

Question 28

Evaluate by interpreting it in terms of areas

Question 29

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.