Math 1700 Distance: Tips for Assignment 4

Published: Thu, 06/25/15

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Did you read my tips on how to study and learn Math 1700?  If not, here is a link to those important suggestions:

Did you see my tips for Assignment 1? Click here.
Did you see my tips for Assignment 2? Click here.
Did you see my tips for Assignment 3? Click here.
Tips for Assignment 4
These are tips for the assignments in the Distance/Online Math 1700 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course.  These assignments are very good (and challenging) practice.  It is possible that you are doing the topics in a different order in the classroom lecture sections, so you may need to wait until later before tackling this assignment.

Here is a link to the actual assignment, in case you don't have it:
Study Lesson 11 (L'Hopital's Rule) and Lesson 12 (Improper Integrals and the Comparison Theorem) from my Calculus 2 book to prepare for this assignment.
Question 1
I don't anticipate any real difficulties here if you have studied Lesson 11.
Question 2
These are all pretty standard improper integrals as shown in Lesson 12.  You will need to use u substitution to solve most of these integrals, so I suggest you solve the indefinite integral first using u sub, then deal with the improper definite integral only once you know the solution to the antiderivative.

Hint: factor the denominator in part (a).
Question 3
Like my Lesson 12, question 2.
Question 4
This is revisiting areas and volumes, but now you have an improper integral.  Note that, by unbounded, they mean the region extends to infinity in the x direction.  If the area in part (a) is unbounded, that just means that you should discover the improper integral diverges.

This is one of the many examples of a region with an infinite area, yet, when it is rotated around an axis, it creates a solid with a finite volume.  Weird, huh?

You may find it helpful to use u sub first.  It is not unheard of to use u sub to change an integral into a form that can then be solved by Integration by parts.  In cases like that, I use a different variable other than u so as not to confuse it with the u in integration by parts. 

For example, try letting t equal square root of x, and compute dt.  Do a t substitution, then you should find that the dt integral you created is an integration by parts problem.
Question 5
Don't let this talk of Laplace Transforms worry you.  That's more advanced calculus.  All this question is saying is sub f(t) = t^2 in place of f(t) in the given integral.  You have now created an improper integral to solve.  Treat s as a constant.  Your solution for this integral is F(s).

Make sure you are being careful to use lowercase f and uppercase F in the correct places in this problem.  They are two different symbols for two different functions.