Name: __________________________ Date: _____________



1.
Find the area of the region bounded by the graphs of the algebraic functions.

A.
B.
C.
D.
E.


2.
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis.

A.
B.
C.
D.
E.


3.
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

A.
B.
C.
D.
E.


4.
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

A.
B.
C.
D.
E.


5.
Find the arc length of the graph of the function over the interval .
A.
B.
C.
D.
E.


6.
Find the area of the surface generated by revolving the curve about the y-axis.

A.
B.
C.
D.
E.


7.
Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

A.
280.8 lb
B.
3,369.6 lb
C.
561.6 lb
D.
1,684.8 lb
E.
93.6 lb


8.
Find the indefinite integral.
A.
B.
C.
D.
E.


9.
Find the definite integral.
A.
104
B.
56
C.
8
D.
64
E.
7


10.
Find the indefinite integral.
A.
B.
C.
D.
E.


11.
Find the indefinite integral.
A.
B.
C.
D.
E.


12.
Find the indefinite integral.
A.
B.
C.
D.
E.


13.
Find the indefinite integral by making the substitution .
A.
B.
C.
D.
E.
None of the above


14.
Use partial fractions to find the integral .
A.
B.
C.
D.
E.


15.
Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule.
A.
B.
0
C.
D.
E.
Limit does not exist.


16.
Evaluate the limit using L'Hopital's Rule if necessary.
A.
B.
C.
D.
0
E.
Limit does not exist.


17.
Evaluate the limit using L'Hopital's Rule if necessary.
A.
B.
C.
D.
E.


18.
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.
A.
diverges
B.
C.
D.
E.


19.
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

an =
A.
Sequence converges to 0
B.
Sequence diverges
C.
Sequence converges to 1
D.
Sequence converges to -1
E.
Sequence diverges to 1


20.
Determine the convergence or divergence of the series.

A.
Cannot be determined by methods of this chapter.
B.
Diverges
C.
Converges


21.
Use the Integral Test to determine the convergence or divergence of the series.

A.
Converges
B.
Diverges
C.
Integral Test inconclusive


22.
Use Theorem 9.11 to determine the convergence or divergence of the series.

A.
Theorem 9.11 is inconclusive
B.
Converges
C.
Diverges


23.
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Direct Comparison Test does not apply


24.
Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Limit Comparison Test does not apply


25.
Use the Ratio Test to determine the convergence or divergence of the series.

A.
Diverges
B.
Converges
C.
Ratio Test is inconclusive


26.
Use the Root Test to determine the convergence or divergence of the series.

A.
Converges
B.
Diverges
C.
Root Test is inconclusive


27.
Find the Maclaurin polynomial of degree 3 for the function.

A.
B.
C.
D.
E.


28.
Find the fourth degree Taylor polynomial centered at c = 7 for the function.

A.
B.
C.
D.
E.


29.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

A.
B.
(–1,1)
C.
[–1,1)
D.
(–6,6)
E.


30.
Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division.

A.
B.
C.
D.
E.
None of the above


31.
Use the power series



to determine a power series, centered at 0, for the function. Identify the interval of convergence.

A.
B.
C.
D.
E.


32.
Use the binomial series to find the Maclaurin series for the function.

A.
B.
C.
D.
E.


33.
Find the vertex, focus, and directrix of the parabola and sketch its graph.

A.
Vertex: (1,–4); Focus: (0,–4); Directrix x = 2

B.
Vertex: (1,–4); Focus: (0,–4); Directrix x = 2

C.
Vertex: (–1,4); Focus: (–2,–4); Directrix x = 0

D.
Vertex: (–1,4); Focus: (–2,–4); Directrix x = 0

E.
Vertex: (1,–4); Focus: (2,–4); Directrix x = 0



34.
Find an equation of the hyperbola with vertices (0,–3), (0,3) and asymptotes .
A.
B.
C.
D.
E.


35.
Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.

A.

B.

C.

D.

E.



36.
Find the arc length of the curve on the given interval.

A.
B.
C.
D.
E.
None of the above


37.
Find the area of the surface generated by revolving the curve about the given axis.



(i) x-axis; (ii) y-axis
A.
(i) ; (ii)
B.
(i) ; (ii)
C.
(i) ; (ii)
D.
(i) ; (ii)
E.
(i) ; (ii)


38.
Convert the rectangular equation to polar form.

A.

B.

C.

D.

E.



39.
Find the points of intersection of the graphs of the equations.

A.
B.
C.
D.
E.
None of the above


40.
Find the length of the curve over the given interval.

A.
B.
C.
D.
E.


41.
Find the area of the surface formed by revolving about the axis the following curve over the given interval.

A.
B.
C.
D.
E.



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