Calculus - Questions for Assignment 6 | MATH 1B, Assignments of Calculus

Material Type: Assignment; Class: Calculus; Subject: Mathematics; University: University of California - Berkeley; Term: Spring 2008;

Typology: Assignments

Pre 2010

Uploaded on 10/01/2009

koofers-user-4hq
koofers-user-4hq 🇺🇸

8 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
February 1st, 2008
Math 1B
1. (a) Find all psuch that R
1xpdx converges.
(b) Find all psuch that R1
0xpdx converges.
2. Why is it important to notice when integrals are improper?
(a) Evaluate the integral
Z1
1
dx
x2.
(b) Now evaluate the integral from part (a) where you “forget” that it
is improper. Explain how the results you get are different, and why
the answer to (b) doesn’t really make sense.
(c) Repeat parts (a) and (b) for
Z1
1
dx
x2/3.
It turns out that failing to notice that an integral is improper will
only run you into trouble if the improper integral diverges, and the
integral computed without noticing improperness does not diverge.
But since plenty of improper integrals diverge, it is still important to
notice when they are improper!
1
pf2

Partial preview of the text

Download Calculus - Questions for Assignment 6 | MATH 1B and more Assignments Calculus in PDF only on Docsity!

February 1st, 2008

Math 1B

1. (a) Find all p such that

1 x

p dx converges.

(b) Find all p such that

0 x

p dx converges.

2. Why is it important to notice when integrals are improper?

(a) Evaluate the integral

dx

x^2

(b) Now evaluate the integral from part (a) where you “forget” that it

is improper. Explain how the results you get are different, and why

the answer to (b) doesn’t really make sense.

(c) Repeat parts (a) and (b) for

dx

x^2 /^3

It turns out that failing to notice that an integral is improper will

only run you into trouble if the improper integral diverges, and the

integral computed without noticing improperness does not diverge.

But since plenty of improper integrals diverge, it is still important to

notice when they are improper!

3. Determine whether or not the following integrals converge

(a)

x^2 +x

x^3 +x^2 − 1 dx

(b)

0 sin^

x^2 dx

4. Determine, with proof, whether the following integrals converge or diverge.

(a)

√^ x x^5 −x^3 +x^2 +x− 1

dx

(b)

√ln^ x x^2 +

dx

(c)

x^2 − 2 x+

x^3 +3x+1 dx

(d)

x^2 − 2 x dx

(e)

√^ ex

x dx