Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
Find the derivative of the algebraic function  .
|
|
|
2.
|
Find the derivative of the function. 
|
|
|
3.
|
Find the derivative of the function.
|
|
|
4.
|
Find the derivative of the function.
|
|
|
5.
|
Find the derivative of the function.
|
|
|
6.
|
Find the derivative of the function.
|
|
|
7.
|
Find the derivative of the function  .
|
|
|
8.
|
Find the derivative of the function  .
|
|
|
9.
|
Find the derivative of the function.
|
|
|
10.
|
Find the derivative of the function.
|
|
|
11.
|
Find the derivative of the function.
|
|
|
12.
|
Find the derivative of the function.
|
|
|
13.
|
Evaluate the derivative of the function  at the point
 .
|
|
|
14.
|
Evaluate the derivative of the function at the given point.
 , 
|
|
|
15.
|
Evaluate the derivative of the function  at the point  .
|
|
|
16.
|
Evaluate the derivative of the function  at the point  .
|
|
|
17.
|
Find an equation to the tangent line for the graph
of f at the given point.
 , 
|
|
|
18.
|
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.
|
|
|
19.
|
Find the second derivative of the
function.
|
|
|
20.
|
Find the second derivative of the function
 .
|
|
|
21.
|
The displacement from equilibrium of an object in
harmonic motion on the end of a spring is  where y is measured in feet and t is the time in seconds.
Determine the position of the object when  . Round your answer to two decimal places.
a. | 0.12 feet | b. | 0.21 feet | c. | 17.53
feet | d. | 0.46 feet | e. | 0.11 feet |
|
|
|
22.
|
The displacement from equilibrium of an object in
harmonic motion on the end of a spring is  where y is measured in feet and t is the time in seconds.
Determine the velocity of the object when  . Round your answer to two decimal places.
a. | 8.00 ft/sec | b. | 4.68 ft/sec | c. | 6.00
ft/sec | d. | 1.00 ft/sec | e. | 5.00 ft/sec |
|
|
|
23.
|
Suppose a 15-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 t =
7 seconds. Round your answer to four decimal places.
a. | 2.5034 radians per second | b. | 3.6185 radians per second | c. | 0.3129 radians per second | d. | 3.1535 radians per second | e. | 4.1724 radians per second |
|
|
|
24.
|
A buoy oscillates in simple harmonic motion
 as waves move
past it. The buoy moves a total of 3.5 feet (vertically) between its low point and its high point. It
returns to its high point every 14 seconds. Write an equation describing the motion of the buoy if it
is at its high point at t = 0.
|
|
|
25.
|
A buoy oscillates in simple harmonic motion
 as waves move
past it. The buoy moves a total of 13.5 feet (vertically) between its low point and its high point.
It returns to its high point every 10 seconds. Determine the velocity of the buoy as a function of
t.
|