Question

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

Answer #1

Determine whether the following sequences converge or diverge.
If a sequence converges, find its limit. If a sequence diverges,
explain why.
(a) an = ((-1)nn)/
(n+sqrt(n))
(b) an = (sin(3n))/(1- sqrt(n))

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

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.

(1 point) Let F(x)=∫o,x sin(6t^2) dt F(x)=∫0xsin(6t^2) dt. The
integrals go from 0 to x
Find the MacLaurin polynomial of degree 7 for F(x)F(x).
Use this polynomial to estimate the value of ∫0, .790 sin(6x^2) dx
∫0, 0.79 sin(6x^2) dx. the integral go from 0 to .790

Determine whether the following sequences converge or diverge.
If it converges, ﬁnd the limit. Must show work
1.)an = nsin(1/n)
2.)an = sin(n)
3).an =4^n /1 + 9^n
4).an = ln(n+1) − ln(n)

Solve the following integrals:
1. The integral of 2 (on top) to 0 (on bottom) of dt / (the
square root of 4+t^2)
2.The integral of 3 (on top) to 2 (on bottom) of dx / (a^2+x^2)
^ 3/2 , a > 0

Do the following sequences converge or diverge? If it converges,
find its limit.
a) an = (4n^3+3n-6) / (5n^26n+2)
b) an = (3n^3+2n-6) / (4n^3+n^2+3n+1)
c) an = (n sin n) / (n^2+4)
d) an = (1/5)^n

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...

Use the following formulas to set up two integrals for the arc
length from (0, 0) to (1, 1). Observe that one of these is an
improper integral.
(I) L
=
b
1 +
dy
dx
2
dx
a
(II) L
=
d
1 +
dx
dy
2
dy
c
L
=
1
√1+49x(23)
dx
0
=
1.4397
L
=
1
√1+94ydy
dy
0
=
1.4397
(c) Find the length of the arc of this curve from
(−1, 1) to...

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.

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