Math 1700 Distance: Tips for Assignment 4

Published: Mon, 02/18/13


 
Please note that I am now taking registrations for my midterm exam prep seminars.  Please click this link for more info and to register, if you are interested:
Grant's Exam Prep Seminars 
 
Did you read my tips on how to do well in Math 1700 Distance?  If not, here is a link to those important suggestions:
How to do Well in Math 1700 Distance 
 
Tips for Assignment 4
Even if you are not taking the distance course, I think it is very useful for all Math 1700 students to attempt these hand-in assignments.  In general, the assignments can be quite demanding and really force you to solidify your math skills.  However, the fact is that the distance course covers the topics in a different order from the classroom lecture sections, so I would not advise classroom students to look at this assignment until they have studied the relevant lessons in class.
 
Here is a link where you can download a copy of Assignment 4:
Math 1700 Distance Assignment 4 (Jan 2013) 
 
Note that you need to 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.  I think you should find this assignment fairly straightforward if you do thoroughly study and do all the Practise Problems I give you in these lessons. 
 
Don't have my book? You can download a sample containing two lessons here (unfortunately, the sample contains lessons 1 and 11):
 
I suggest that, if you are comparing an improper integral to a p-integral, you may actually want to prove the specific p-integral converges or diverges rather than just say so because it is a p-integral (in case the prof wants to see thorough proofs).  Alternatively, just be more specific than saying "p-integral."  For example, if you had the integral from 0 to 3 of dx/x3 which we know diverges to infinity, say that the integral diverges to infinity since integral from 0 to a of dx/xp diverges to infinity if p>1.  (Obviously, use the integral symbol.)
 
When he talks about the area being unbounded in question 4(a), he means show that the integral diverges.  Whereas, apparently the integral in 4(b) converges.
 
Question 5 is going to take a technique of integration to solve.  Note that you would consider s to be a constant coefficient while solving the integral.