1) Find
a) ![](images/Calc_AB_Section1_437.gif)
b) ![](images/Calc_AB_Section1_438.gif)
c) ![](images/Calc_AB_Section1_439.gif)
d) ![](images/Calc_AB_Section1_440.gif)
*e) ![](images/Calc_AB_Section1_441.gif)
2) The function g is defined by the formula
Find the slope of the tangent line at x = 1.
a) ![](images/Calc_AB_Section1_443.gif)
*b) ![](images/Calc_AB_Section1_444.gif)
c) ![](images/Calc_AB_Section1_445.gif)
d) ![](images/Calc_AB_Section1_446.gif)
e) ![](images/Calc_AB_Section1_447.gif)
3) Find
*a) 4
b) ![](images/Calc_AB_Section1_448.gif)
c) 1
d) ![](images/Calc_AB_Section1_449.gif)
e) The limit does not exist.
4) The given function f has a removable discontinuity at x = -5. Find A.
a) -15
b) -5
c) 5
d) -4
*e) -25
5) If f ' (x) =
which of the following is true about y = f (x)?
*a) f has a point of inflection at x = 2 and a local maximum at x = 8.
b) f has a local maximum at x = 2 and a local minimum at x = 8.
c) f has a local minimum at x = 2 and a local maximum at x = 8.
d) f has a point of inflection at x = 2 and a local minimum at x = 8.
e) f has a local minimum at x = 2 and a point of inflection at x = 8.
6) Find f ' (9), given that
a) ![](images/Calc_AB_Section1_454.gif)
b) ![](images/Calc_AB_Section1_455.gif)
*c) ![](images/Calc_AB_Section1_456.gif)
d) ![](images/Calc_AB_Section1_457.gif)
e) ![](images/Calc_AB_Section1_458.gif)
7) Find the average value of the given function f over the interval [0, 4].
a) ![](images/Calc_AB_Section1_460.gif)
*b) ![](images/Calc_AB_Section1_461.gif)
c) ![](images/Calc_AB_Section1_462.gif)
d) ![](images/Calc_AB_Section1_463.gif)
e) ![](images/Calc_AB_Section1_464.gif)
8) Find f ' (0), given that
a) ![](images/Calc_AB_Section1_466.gif)
b) ![](images/Calc_AB_Section1_467.gif)
*c) ![](images/Calc_AB_Section1_468.gif)
d) ![](images/Calc_AB_Section1_469.gif)
e) ![](images/Calc_AB_Section1_470.gif)
9) Find f ' (1), given that
a) ![](images/Calc_AB_Section1_472.gif)
b) ![](images/Calc_AB_Section1_473.gif)
c) ![](images/Calc_AB_Section1_474.gif)
*d) ![](images/Calc_AB_Section1_475.gif)
e) ![](images/Calc_AB_Section1_476.gif)
10) Find
a) The limit does not exist.
b) -10
c) 1
*d) 0
e) 10
11) Given the following curve, find
.![](images/Calc_AB_Section1_478.gif)
a) ![](images/Calc_AB_Section1_479.gif)
b) ![](images/Calc_AB_Section1_480.gif)
c) ![](images/Calc_AB_Section1_481.gif)
*d) ![](images/Calc_AB_Section1_482.gif)
e) ![](images/Calc_AB_Section1_483.gif)
12) Given that f(x) = 7sin2(4x), find f ''
.
a) ![](images/Calc_AB_Section1_485.gif)
b) ![](images/Calc_AB_Section1_486.gif)
c) ![](images/Calc_AB_Section1_487.gif)
*d) ![](images/Calc_AB_Section1_488.gif)
e) ![](images/Calc_AB_Section1_489.gif)
13) Find the midpoint rectangular approximation for
using 3 subintervals of equal length.
a) ![](images/Calc_AB_Section1_491.gif)
b) ![](images/Calc_AB_Section1_492.gif)
*c) ![](images/Calc_AB_Section1_493.gif)
d) ![](images/Calc_AB_Section1_494.gif)
e) ![](images/Calc_AB_Section1_495.gif)
14) Find the derivative of the function y = cos-1 (3x).
a) -3sin-1(3x)
b) ![](images/Calc_AB_Section1_506.gif)
c) ![](images/Calc_AB_Section1_507.gif)
*d) ![](images/Calc_AB_Section1_504.gif)
e) ![](images/Calc_AB_Section1_505.gif)
15) Find
a) ![](images/Calc_AB_Section1_509.gif)
b) ![](images/Calc_AB_Section1_510.gif)
c) ![](images/Calc_AB_Section1_511.gif)
*d) ![](images/Calc_AB_Section1_512.gif)
e) ![](images/Calc_AB_Section1_513.gif)
16) Find the equation of the tangent line to the given curve at the point (0, 9).
a) ![](images/Calc_AB_Section1_515.gif)
b) ![](images/Calc_AB_Section1_516.gif)
c) ![](images/Calc_AB_Section1_517.gif)
*d) ![](images/Calc_AB_Section1_518.gif)
e) ![](images/Calc_AB_Section1_519.gif)
17) If g(f(x)) = x, g(5) = 2 and g'(5) = 13, then f '(2) is
*a) ![](images/Calc_AB_Section1_520.gif)
b) ![](images/Calc_AB_Section1_521.gif)
c) ![](images/Calc_AB_Section1_522.gif)
d) ![](images/Calc_AB_Section1_523.gif)
e) ![](images/Calc_AB_Section1_524.gif)
18) Given that ![](images/Calc_AB_Section1_525.gif)
find ![](images/Calc_AB_Section1_526.gif)
*a) ![](images/Calc_AB_Section1_527.gif)
b) ![](images/Calc_AB_Section1_528.gif)
c) ![](images/Calc_AB_Section1_529.gif)
d) ![](images/Calc_AB_Section1_530.gif)
e) ![](images/Calc_AB_Section1_531.gif)
19) Which of the following differential equations corresponds to the slope field shown in the figure below?
![](images/image_19.gif)
*a) ![](images/Calc_AB_Section1_532.gif)
b) ![](images/Calc_AB_Section1_533.gif)
c) ![](images/Calc_AB_Section1_534.gif)
d) ![](images/Calc_AB_Section1_535.gif)
e) ![](images/Calc_AB_Section1_536.gif)
20) Given the following function, with x > 0, on which interval is the function decreasing?
*a) ![](images/Calc_AB_Section1_538.gif)
b) ![](images/Calc_AB_Section1_539.gif)
c) ![](images/Calc_AB_Section1_540.gif)
d) ![](images/Calc_AB_Section1_541.gif)
e) ![](images/Calc_AB_Section1_542.gif)
21) Find the area of the region enclosed by the graphs of
and
*a) ![](images/Calc_AB_Section1_545.gif)
b) ![](images/Calc_AB_Section1_546.gif)
c) ![](images/Calc_AB_Section1_547.gif)
d) ![](images/Calc_AB_Section1_548.gif)
e) ![](images/Calc_AB_Section1_549.gif)
22) Find
a) ![](images/Calc_AB_Section1_551.gif)
b) ![](images/Calc_AB_Section1_552.gif)
c) ![](images/Calc_AB_Section1_553.gif)
d) ![](images/Calc_AB_Section1_554.gif)
*e) ![](images/Calc_AB_Section1_555.gif)
23) The region bounded by the following graph![](images/Calc_AB_Section1_556.gif)
and the x-axis, for 0 < x <
, is rotated about the line y = -4. The volume of this solid can be represented by:
a) ![](images/Calc_AB_Section1_558.gif)
b) ![](images/Calc_AB_Section1_559.gif)
c) ![](images/Calc_AB_Section1_560.gif)
*d) ![](images/Calc_AB_Section1_561.gif)
e) ![](images/Calc_AB_Section1_562.gif)
24) The side of a cube is expanding at a constant rate of 4 inches per second. What is the rate of change of the volume, in in3 per second, when the total surface area of the cube is 54 in2?
a) 36
*b) 108
c) 72
d) 12
e) 216
25) The solution to the differential equation![](images/Calc_AB_Section1_563.gif)
with the initial condition y(0) = 3 is
a) ![](images/Calc_AB_Section1_564.gif)
*b) ![](images/Calc_AB_Section1_565.gif)
c) ![](images/Calc_AB_Section1_566.gif)
d) ![](images/Calc_AB_Section1_567.gif)
e) ![](images/Calc_AB_Section1_568.gif)
26)
=
*a) ![](images/Calc_AB_Section1_570.gif)
b) ![](images/Calc_AB_Section1_571.gif)
c) ![](images/Calc_AB_Section1_572.gif)
d) ![](images/Calc_AB_Section1_573.gif)
e) ![](images/Calc_AB_Section1_574.gif)
27) The position of a particle moving along a horizontal line is given by
What is the maximum speed of the particle for 0 < t < 10?
a) 54
b) 98
*c) 294
d) 162
e) 18
28) Using the information below, find
when t = 0.![](images/Calc_AB_Section1_577.gif)
![](images/Calc_AB_Section1_578.gif)
a) ![](images/Calc_AB_Section1_580.gif)
b) ![](images/Calc_AB_Section1_581.gif)
c) ![](images/Calc_AB_Section1_582.gif)
d) ![](images/Calc_AB_Section1_583.gif)
*e) ![](images/Calc_AB_Section1_584.gif)