Question

Determine whether the improper integral from 5 to infinity 3/square root x dx converges or diverges, and find the value if it converges.

Select the correct choice below and fill in any answer boxes within your choice.

A. The value of the integral

B.The integral diverges.

Answer #1

A) Use the Comparison Test to determine whether integral from 2
to infinity x/ sqrt(x^3 -1)dx is convergent or divergent.
B)Use the Comparison Test to determine whether the integral from
2 to infinity (x^2+x+2)/(x^4+x^2-1) dx is convergent or
divergent.

Determine whether the series
Summation from n equals 0 to infinity e Superscript negative 5
n∑n=0∞e^−5n
converges or diverges. If it converges, find its sum.
Select the correct choice below and, if necessary, fill in the
answer box within your choice.
A.The series converges because
ModifyingBelow lim With n right arrow infinitylimn→∞
e Superscript negative 5 ne−5nequals=0.
The sum of the series is
nothing.
(Type an exact answer.)
B.The series diverges because it is a geometric series with
StartAbsoluteValue r...

Prove that the integral from 0 to Infinity (sin^2(x)e^-x)dx
converges using the comparison test.

Explain whether the following integrals converge or not. If the
integral converges, find the value. If the integral does not
converge, describe why (does it go to +infinity, -infinity,
oscillate, ?)
i) Integral from x=1 to x=infinity of x^-1.4 dx
ii) Integral from x=1 to x=infinity of 1/x^2 * (sin x)^2 dx
iii) Integral from x=0 to x=1 of 1/(1-x) dx

Determine whether the sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.) a n = n 3 /n + 2

Determine the convergence or divergence if each integral by
using a comparison function. Show work using the steps below:
A. Indicate the comparison function you are using.
B. Indicate if your comparison function is larger or smaller
than the original function.
C. Indicate if your comparison integral converges or diverges.
Explain why.
D. State if the original integral converges or diverges. If it
converges, you don’t need to give the value it converges to.
11. integral from 1 to infinity...

Find the square root that is a real number.
negative StartRoot negative 4
EndRoot
Select the correct choice below and, if necessary, fill in the
answer box within your choice.
A.
The real number square root is
nothing
.
(Simplify your answer. Type an integer or a fraction.)
B.
The square root is not a real number.

Use the ratio test to determine whether∑n=12∞n2+55n
converges or diverges.
(a) Find the ratio of successive terms. Write your
answer as a fully simplified fraction. For n≥12,
limn→∞∣∣∣an+1an∣∣∣=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞
as infinity and −∞ as -infinity. If the limit does
not exist, enter DNE.
limn→∞∣∣∣an+1an∣∣∣ =
(c) By the ratio test, does the series converge,
diverge, or is the test inconclusive?

1a) Evaluate the limit as x goes to infinity using l'hopitals
rule
(x^-1/3)/sin(1/x)
1b) Evaluate the improper integral (if convergent find it's
value)
(secx-tanx)dx where a= 0 and b=pi/2

Determine whether each of the following series converges or not.
(Name the test you use. You do not have to evaluate the sums of
these series). Please write as big and neatly as possible
in your answer, demonstrating all steps.
a) Sum infinity n = 1 of square root n/n^3+1
b) Sum infinity n = 2 of 1/nln(n)

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