MAT 302 Assignment Problem 9.3 | Borough of Manhattan Community College
- Borough of Manhattan Community College / MAT 302
- 19 Jun 2021
- Price: $12
- Mathematics Assignment Help / Calculus
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∞66lnn
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.