Mobius 3 assignment PDF

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Mobius 3 assignment...

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1/31/2020

University of Ottawa -

Assignment Worksheet

Online Homework System

1/31/20 - 5:12:55 PM EST

Name:

____________________________

Class:

MAT 1332 - Winter 2020 - All sections

Class #:

____________________________

Section #:

____________________________

Instructor: Benoit Dionne

Assignment: Assignment 3

Question 1: (1 point) We wish to compute

(i) We begin by factorizing the denominator of the rational function. We get

for

. What are

and

____________ ,

? ____________

(ii) Next, we express the fraction in the form

Give the exact values of __________ ,

,

and

.

__________ ,

__________

(iii) Finally, we use this partial fraction decomposition to compute the integral. Give its approximate value with

decimal places.

____________

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Question 2: (1 point) We wish to compute

(i) We begin by noting that

where

is a polynomial of degree two with no real roots. We can thus write

Give the exact values of

,

____________ ,

and

.

____________ and

____________

(ii) Finally, we use this partial fraction decomposition to compute the integral. Give its approximate value to

decimal places.

____________

Question 3: (1 point) To compute the indefinite integral

We begin by rewriting the rational function in the form

(i) Give the exact values of __________ ,

and

.

__________

(ii) Using your new expression, compute __________

where

represents the integration constant. Do not include the integration constant in your answer , as we have included it for you.

Important: Here we ask that you use absolute values inside of logarithms, so as to maximize the domain for which your antiderivative is valid. You write for the natural logarithm of the absolute value of x (not "ln|x|" !).

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Question 4: (1 point) Compute the indefinite integral

__________

where

represents the integration constant. Do not include the integration constant in your answer , as we have included it for you.

Important: Here we ask that you use absolute values inside of logarithms, so as to maximize the domain for which your antiderivative is valid. You write for the absolute value of x.

Question 5: (1 point) Study the convergence of

and, if the integral is convergent, give its value. a) The integral is __________. b) If the integral converges, its exact value is __________. Write Diverges if the integral is divergent.

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Question 6: (1 point) A) Study the convergence of

and if the integral is convergent, give its value. A.1) The integral is __________. A.2) If the integral converges, its exact value is __________. Input if the integral is divergent. B) Study the convergence of

and if the integral is convergent, give its value. B.1) The integral is __________. B.2) If the integral converges, its exact value is __________. Input if the integral is divergent.

Question 7: (1 point) Study the convergence of

and if the integral is convergent, give its value. a) The integral is __________. b) In the case that it is convergent, its approximate value within Input if the integral is divergent.

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is ____________

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Question 8: (1 point) Study the convergence of

and, if the integral is convergent, find its value. a) The integral is __________. b) In the case that it is convergent, express its value as a multiple __________ Input

of

and give the exact value of

:

if the integral is divergent.

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