Deck 18: Final Exam

Question 1

If , evaluate the difference quotient .

A)
B)h
C)
D)
E)None of these

Answer 1

None of these

Question 2

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .

A)
B)diverges
C)
D)
E)

Answer 2

Question 3

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

A)
B)
C)
D)
E)

Answer 3

Question 4

Solve the initial-value problem.

A)
B)
C)
D)
E)

Question 5

A piece of wire m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

A) m
B) m
C) m
D) m
E) m

Question 6

Evaluate the integral.

A)
B)
C)
D)
E)

Question 7

If an equation of the tangent line to the curve at the point where

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

Question 8

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

A)
B)
C)
D)
E)

Question 9

The graphs of and are given. For what values of x is ?

A)-4, 12
B)4, 2
C)
D)0
E)

Question 10

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. ,

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

Question 11

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

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

Question 12

Find the average value of the function on the interval . Round your answer to 3 decimal places.

A)0.3
B)
C)0.288
D)6.228
E)12

Question 13

The height (in meters) of a projectile shot vertically upward from a point m above ground level with an initial velocity of 25.48 m/s is after t seconds. a) When does the projectile reach its maximum height? b) What is the maximum height?

A)
B)
C)
D)
E)

Question 14

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

A)
B)
C)
D)
E)

Question 15

Find the length of the curve.

A)
B)25.05
C)13.05
D)36.05
E)None of these

Question 16

How would you define in order to make f continuous at ?

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

Question 17

The masses are located at the point . Find the moments and and the center of mass of the system. ;

A)
B)
C)
D)
E)

Question 18

The acceleration function (in m / s²) 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)

Question 19

Which equation does the function satisfy?

A)
B)
C)
D)
E)

Question 20

Evaluate the integral.

A)
B)
C)
D)
E)

Question 21

Find the area of the region that is bounded by the given curve and lies in the specified sector.

Question 22

Find the sum of the series.

A)
B)
C)
D)
E)

Question 23

If , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

Question 24

The graphs of and are given.
Find the values of and .

Question 25

Find the unit tangent vector for the curve given by .

Question 26

Calculate the given quantities if

Question 27

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

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

Question 28

Find the length of the curve. ,

Question 29

Find the volume of the resulting solid if the region under the curve from to is rotated about the x-axis. Round your answer to four decimal places.

Question 30

Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1).

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

Question 31

The top of a ladder slides down a vertical wall at a rate of 0.1m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

Question 32

Find the local and absolute extreme values of the function on the given interval. ,

Question 33

Use Euler's method with step size 0.1 to estimate , where is the solution of the initial-value problem. Round your answer to four decimal places.

Question 34

If , evaluate .

A)
B)
C)
D)
E)

Question 35

Use spherical coordinates. Evaluate , where is the ball with center the origin and radius .

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

Question 36

Find for the function .

A)
B)
C)
D)
E)

Question 37

Find the curvature of .

A)
B)
C)
D)
E)

Question 38

Evaluate the line integral.

A)
B)
C)
D)
E)

Question 39

Evaluate the integral using the indicated trigonometric substitution.

Question 40

Solve the initial-value problem.

Question 41

Find the volume of the given solid.
Under the paraboloid and above the rectangle .

Question 42

Find the volume of the given solid.
Under the paraboloid and above the rectangle .

Question 43

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Question 44

Find all the second partial derivatives of