MAT 302 Assignment Problem 9.3

MAT 302 Assignment Problem 9.3 | Borough of Manhattan Community College

9.3 The Integral Test and p-series

Question 1

(1 point) Compute the value of the following improper integral. If it converges, enter its value. Enter infinity if it diverges to ∞∞, and -infinity if it diverges to −∞−∞. Otherwise, enter diverges.

Question 2

Use the Integral Test to determine whether the infinite series is convergent.

∑n=5∞2ne−n2

Fill in the corresponding integrand and the value of the improper integral.
Enter inf for ∞∞, -inf for −∞−∞, and DNE if the limit does not exist.

Compare with 

By the Integral Test,

the infinite series ∑n=5∞2ne−n2

Question 3

Use the Integral Test to determine whether the infinite series is convergent.

∑n=1∞66lnn∑n=1∞66ln⁡n

Fill in the corresponding integrand and the value of the improper integral.
Enter inf for ∞∞, -inf for −∞−∞, and DNE if the limit does not exist.

Question 4

(1 point)

Use the Integral Test to determine whether the infinite series is convergent.

∑n=1∞n−45∑n=1∞n−45

Fill in the corresponding integrand and the value of the improper integral.
Enter inf for ∞∞, -inf for −∞−∞, and DNE if the limit does not exist.

Question 5

(1 point) Use the integral test to determine whether each of the following series converges or diverges. For each, fill in the integrand and the value of the integral. Enter diverges if the integral diverges. Then indicate the convergence of the sum.

A.    ∑n=1∞18n

Question 6

(1 point) Compute the value of the following improper integral. If it converges, enter its value. Enter infinity if it diverges to ∞∞, and -infinity if it diverges to −∞−∞. Otherwise, enter diverges.

Question 7

(1 point) a) Find the value of the integral

b) Determine whether the series

Question 8

(1 point) Test each of the following series for convergence by the Integral Test. If the Integral Test can be applied to the series, enter CONV if it converges or DIV if it diverges. If the integral test cannot be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the Integral Test cannot be applied to it, then you must enter NA rather than CONV.)

Question 9

Question 10

(1 point) Determine the convergence or divergence of the p-series.
Note: Enter CONV if it converges and DIV if it diverges.

Question 11

(1 point) Use Theorem 9.11 on the textbook p.607 to determine the convergence or divergence of the p-series.
Note: Enter CONV if it converges and DIV if it diverges.

Question 12

(1 point) Use Theorem 9.11 on the textbook p.607 to determine the convergence or divergence of the p-series.
Note: Enter CONV if it converges and DIV if it diverges.