Practice Unit 3. Have your sheet of series expansions ready.



1.
Use the Integral Test to determine the convergence or divergence of the series.

A.
Converges
B.
Diverges
C.
Integral Test inconclusive


2.
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Direct Comparison Test does not apply


3.
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Direct Comparison Test does not apply


4.
Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Limit Comparison Test does not apply


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


6.
Which of the series below should be used in the Limit Comparison Test to determine
whether the series converges or diverges? Does this series converge or diverge?
A.
compare to ; converges
B.
compare to ; diverges
C.
compare to ;
D.
compare to ; converges
E.
compare to ; diverges


7.
Consider the series .
Review the Alternating Series Test to determine which of the following statements is true for the given series.
A.
Since , the series diverges.
B.
Since , the Alternating Series Test cannot be applied.
C.
Since for some n, the series diverges.
D.
Since for some n, the Alternating Series Test cannot be applied.
E.
The series converges.


8.
Use the Alternating Series Test (if possible) to determine whether the series converges or diverges?
A.
B.
C.
Alternating Series Test cannot be applied


9.
Determine whether the series converges absolutely, converges conditionally, or diverges.
A.
B.
C.
diverges


10.
Use the Ratio Test to determine the convergence or divergence of the series.

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


11.
Use the Ratio Test to determine the convergence or divergence of the series.

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


12.
Use the Root Test to determine the convergence or divergence of the series.

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


13.
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

A.
Diverges; Ratio Test
B.
Diverges; Theorem 9.9 (nth Term Test for Divergence)
C.
Converges; p-series
D.
Converges; Integral Test
E.
Both A and B
F.
Both C and D


14.
Find the Maclaurin polynomial of degree 3 for the function.

A.
B.
C.
D.
E.


15.
Find the fourth degree Maclaurin polynomial for the function.

A.
B.
C.
D.
E.


16.
Find the radius of convergence of the power series.

A.
0
B.
10
C.
20
D.
100
E.


17.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

A.
(–3,3)
B.
[–3,3]
C.
D.
{0}
E.


18.
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


19.
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.


20.
Use the definition to find the Taylor series (centered at c) for the function.

A.
B.
C.
D.
E.


21.
Use the definition to find the Taylor series (centered at c) for the function.

A.
B.
C.
D.
E.



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