Chapter 9 Practice Test



1.
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

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


2.
Determine the convergence or divergence of the series.

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


3.
Use the Integral Test to determine the convergence or divergence of the series.

A.
Integral Test inconclusive
B.
Diverges
C.
Converges


4.
Use Theorem 9.11 to determine the convergence or divergence of the series.

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


5.
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Direct Comparison Test does not apply


6.
Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Limit Comparison Test does not apply


7.
Determine whether the series converges absolutely, converges conditionally, or diverges.
A.
B.
C.
converges conditionally


8.
Use the Ratio Test to determine the convergence or divergence of the series.

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


9.
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

A.
Converges; p-series
B.
Diverges; p-series
C.
Diverges; Ratio Test
D.
Converges; Integral Test
E.
Both A and C
F.
Both B and D


10.
Find the Maclaurin polynomial of degree 4 for the function.

A.
B.
C.
D.
E.


11.
Find the fourth degree Maclaurin polynomial for the function.

A.
B.
C.
D.
E.


12.
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.
C.
D.
E.


13.
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


14.
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.


15.
Use the definition to find the Taylor series (centered at c) for the function.

A.
B.
C.
D.
E.


16.
Use the binomial series to find the Maclaurin series for the function.

A.
B.
C.
D.
E.



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