Today we reviewed the topics we have been working on this chapter: L'Hopital's rule, comparing relative rates of growth, and improper integrals. Homework is the pink worksheet.
After today, you should be able to identify and improper integral and explain why it is improper. You should also be able to rewrite it as the limit of a proper integral and determine if the integral converges or diverges. Homework is p. 442 #3,6,8.
Today we learned about improper integrals. Homework is p. 442 Quick Response #1,2,4,5,6 (these should be review problems to get you thinking) and Exercises #2-6 (these are the types of problems we learned today). You only need to do the ones that have infinity as one of the limits of integration. We will learn how to deal with the ones that have infinite discontinuities tomorrow.
Here is the recap of what we have done since last Thursday.
Friday 4/22: We practiced using L'Hopital's rule. p. 424 #15-41 odd Monday 4/25: We learned how to compare rates of growth of different functions as x gets very large. Homework is p. 431 #1-21 odd. Some problems are not a straight plug and chug. You will have to think about what the function is doing as x gets very large. Tuesday 4/26: More practice comparing growth rates. Homework is p. 431 #2-22 even. Today we learned how to rewrite functions into a form that would allow us to apply L'Hopital's rule. For some problems we use algebraic techniques to get the function into the form we need. For other problems we need to use logarithms. Homework is to complete the right column of problems from yesterday's worksheet. Tomorrow is a work day to practice these techniques.
Today we learned L'Hopital's rule for finding limits of rational functions when direct substitution gives an indeterminate form. Homework is a worksheet, only do the problems in the left column.
Today we worked on another worksheet to review algebraic methods of finding limits.
Today we reviewed different techniques for evaluating limits of functions, including substitution, algebraic manipulation, tables, and graphs. Homework was a worksheet that is due tomorrow. Solutions are available in the chapter 8 folder on GD.
Solutions to the review assignment are posted. The solutions to the group quiz (before spring break) are also on google drive. Today we learned the formula to find the length of a curve. Homework is p. 399 #1-9 odd (skip #7) and 11,12. Keep working on your review problems. We'll go over the bothersome ones in class tomorrow.
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