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 read my Tips for Assignment 1?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 2?  If not, here is a link to those important suggestions:

These are tips for the third assignment 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:

Note that you need to study Lesson 9 (Integrating by Trig Substitution), Lesson 10 (Integrating Rational Functions), and Lesson 11 (L'Hopital's Rule) from my Calculus 2 book to prepare for this assignment!  Some of the integrals you have been given in this assignment will be very demanding.

Don't have my book?  You can download a free sample of my book and audio lectures containing Lesson 1 and 11:

These are all pretty complicated integrals to solve.  Here are some hints:

Part (a) is pretty standard stuff if you have studied Lesson 9.

Part (b) is also Lesson 9.  Complete the Square.

Part (c) is from outer space. Try multiplying top and bottom by a trig function in order to make one of those two trig functions in the denominator disappear.

Part (d) is obviously a count-down type from Lesson 10. 

Part (e) is the worst count-down type from Lesson 10.  You may even need to resort to trig substitution to solve one of your partial fractions integrals.  Rather than solve the unknown constants by subbing in values of x, the technique I prefer in my book, this problem works best if you, instead, leave the x values unsubstituted and instead just get rid of the denominators on both sides of the equation and multiply all the terms out on the right hand side.  Then, compare like terms.  Which is to say, compare the x-cubed term on the left hand side to the x-cubed term on the right hand side to solve an unknown.  Then compare the x-squared term on the left to the x-squared term on the right to solve another unknown.  Continue in that way, and you should find all the unknowns solve without much fuss.

Part (a) is a very challenging Lesson 11 problem.  As their hint suggests, instead of solving the given limit, solve the limit of e raised to the power of the given function.  As an additional hint, note that e raised to the power of "a-b", is also expressible as e^a divided by e^b.

Don't forget, if the answer to your limit you create is L, then the answer for the limit they actually gave you is lnL.

Parts (b) and (c) are much more ordinary Lesson 11 problems.