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Don't have my book or audio lectures? You can download a sample containing some of these lessons here: Did you read my tips on how to study and learn Math 1700?
If not, here is a link to those important suggestions: These are tips for the first 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: 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.
Part (a)
Like my Lesson 9, question 1.
Part (b) Like my Lesson 9, question 1. Complete the square.
Part (c) Like my Lesson 10, question 1. Can solve two of the unknown constants by Cover-Up
Method, leaving two more unknowns to solve.
Part (d) Like my Lesson 10, question 1. Unfortunately, you will have 4 unknown constants and won't be able to solve any of them by cover-up method.
Rather
than solve the unknown constants by subbing in values of x, the technique I illustrate in my book (which would create a four equations with four unknowns problem), 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.
You will get something like this (this is a similar example, but not identical):
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. Like
so:
Continue like this to set up equations for all the x terms and for all the constant terms (the terms that don't have an x). Part (a)
Like my Lesson 11, question 1. Substitute the hint you are given in place of that x in the first term. That now creates a difference between two logarithms. Use log laws to combine that into the log of a
quotient. Ignore the log in front of the quotient, and solve the limit of the quotient alone. Then, you can now solve the given limit by doing the log of your answer.
Part (b)
Like my Lesson 11, question
1.
Part (c)
Like my Lesson 11, question 1. |
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