1) Find

a)
b)
*c)
d)
e)
2) If
which of the following is true about y = f (x)?
*a) f has a point of inflection at x = 6 and a local maximum at x = 9.
b) f has a local maximum at x = 6 and a local minimum at x = 9.
c) f has a local minimum at x = 6 and a local maximum at x = 9.
d) f has a point of inflection at x = 6 and a local minimum at x = 9.
e) f has a local minimum at x = 6 and a point of inflection at x = 9.
3) A curve is described by parametric equations
where t > 0. Give an expression for

a)
*b)
c)
d)
e)
4) Give the value for

*a)
b)
c)
d)
e)
5) Which of the following series converge?
I.

II.

III.

a) II only
*b) I, II and III
c) II and III only
d) I and II only
e) I only
6) If g(f(x)) = x, g(7) = 2 and g'(7) = 12, then f '(2) is
*a)
b)
c)
d)
e)
7) If f is a differentiable function and f(0) = -3 and f(2) = 6, then which of the following must be true?
I. There exists a c in [0,2] where f(c) = 0.
II. There exists a c in [0,2] where f ' (c) = 0.
III. There exists a c in [0,2] where f ' (c) = 9/2.

a) II only
b) I only
*c) I and III only
d) II and III only
e) I, II and III
8) Evaluate

a)
b)
c)
d)
*e)
9) Find the area enclosed by the graphs of
and the y-axis.
a)
b)
c)
d)
*e)
10) What is the minimum value of the function

a)
*b)
c)
d)
e)
11) Give the value of

*a)
b)
c)
d)
e)
12) The side of a cube is expanding at a constant rate of 4 inches per second. What is the rate of change of the surface area, in in2 per second, when the volume of the cube is 64 in3?
a)
b)
c)
*d)
e)
13) Give the area inside one petal of the polar graph of

a)
*b)
c)
d)
e)
14) Give the solution to the initial value problem

a)
b)
c)
*d)
e)
15) 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)
b)
c)
d)
*e)
16) =
a)
b)
c)
d)
*e)
17) Define the function
for x > 0. Give the interval on which the function is increasing.
a)
b)
c)
*d)
e)
18)

Which of the following differential equations correspond to the slope field shown in the figure above?
a)
b)
c)
*d)
e)
19) Evaluate

a)
b)
c)
d)
*e)
20) If thenis
a)
b)
*c)
d)
e)
21) Find the area of the region enclosed by the graph of
and the line

a)
*b)
c)
d)
e)
22) Suppose
and
What is dz/dt when t = 1?
a)
b)
c)
*d)
e)
23) Evaluate

a)
b)
c)
*d)
e)
24) Give an equation for the tangent line to the parametric curve
at t = 0.
a)
b)
c)
*d)
e)
25) Evaluate

a)
b)
c)
d)
*e)
26) The region bounded by
and the x-axis, for 0 < x < , is rotated about the line y = -2. The volume of this solid can be represented by:
a)
*b)
c)
d)
e)
27) Give the third degree Taylor polynomial about x = 1 of

a)
b)
c)
d)
*e)
28) Which of the following integrals gives the length of the graph of
for x between 0 and 2?
*a)
b)
c)
d)
e)