Write an outline for sections 6.2-6.4. Work on the solutions to Section 6.1: exercises 21 and 36, Section 6.2: exercises 54 and 93, Section 6.3: exercises 44 and 64, and Section 6.4: exercises 26 and 74. Section 6.1:exercuses 21 and 36 Section 6.2: exercises 54 and 93 Section 6.3: exercises 44 and 64 Section 6.4: exercises 26 and 74. Instructions Write an outline for sections 6.2 to 6.4. Work on the solutions to Section 6.1: exercises 21 and 36, Section 6.2: exercises 54 and 93, Section 6.3: exercises 44 and 64, and Section 6.4: exercises 26 and 74. Submit a report in the comment box of this homework detailing your progress and status toward completion. The end of the report should contain a brief summary stating whether the outlines and exercises were given sufficient effort (whether the correct answer was derived or not). NOTE: I do not need to see your work - I only want you to report on your homework activity (for each problem, whether it was found to be difficult, obvious, easy/hard, whether you at first had troubles but eventually found the/a solution, etc.) I would like you to document (i.e., report on) your homework experience. You can grade your own work via the solutions I provide. I award 3 pts for your reported work on the outlined sections (3pts per section outline) and 3pts for each exercise problem reported. The homework has two parts, the outline and the problems. Please note that you do not need to upload the outlines, you can simply tell me which sections you completed an outline for. The second part of the homework is the more important one. The problems assigned are designed to prepare you for the quiz. I would like you to tell me which problems you attempted and what level of effort you had to put into each problem. Basically, just tell me if the problem was easy for you or difficult, for example, 6.1.36 was extremely difficult for me, I needed four attempts to solve the problem and am not confident in my solution. This needs to be in the comment section of the submission. I will post solutions to all assigned problems immediately after the due date in the content section of the course. Here is an example of what I want for homework submissions: 11.1: 11) This problem was easy and took only a few steps get the numbers in the sequence. 26) This did not take too long and I was able to confirm my answer. 35) Ah! The answer was obvious after looking at the problem for a few seconds. 38) This problem was also easy. Just had to remember L'Hospital's Rule. 42) This one took me more time than the others but still arrived at the answer without much trouble. 11.2: 24) This problem was easy. 30) Again, this problem was also easy but take a few more steps. 34) At first I had trouble with this problem but then realized my error. Still not very difficult though. 38) Easy problem. 59) I had trouble with this one. I was approaching it incorrectly. I had to use the answer in the back to assist with solving the problem. 11.3: 6) This problem took me a great amount of time and I am uncertain of my answer. 7) Easy, solved in a few steps. 16) Not too difficult. 20) This problem was hard for me and I must be doing an error somewhere that I don't see. 30) Difficult and I did not reach a solution. 11.4. 10) Easy and did not take much time. 11) I had trouble with this problem. 20) This problem took me a large amount of time but I did reach the solution. 32) I had trouble with this problem and did not reach a solution. 38) This problem was surprisingly easy. I felt as if I did more reading in section 11.1 than work. The work in the section was not particularly difficult for me to grasp. The sections 11.1-11.3 were not very difficult. It did not take much to understand the concepts presented in them. The problems themselves were also not very difficult. I would rate them among the easier sections I have done in calculus. In sections 11.4 it did get more complicated and the problems were significantly more difficult but not overly challenging. I felt like I gave this assignment plenty of effort. It took a large amount of reading time and work time! Not having to write out the outlines were a plus as well since I write the most important information from the sections on the same pages that I do my work on. I feel like I am writing down most of the information twice, once in the outline and again on my work pages. Hope this helps. Outline for Section 6.1, \"Inverse Functions\" I. Inverse Functions A. Representation of functions 1. Table 2. Graph 3. Mathematical expression B. Definition: A function has an inverse over its domain if it is one-to-one, or equally written, 1:1. C. Definition: A function is 1:1 if it never takes on the same value twice, i.e., it passes the horizontal line test provided we have a graph of the function. D. Domain/Range of the inverse function: If the domain/range of the function is given by D and R, respectively, then the domain/range of its inverse, written here as Dinv/Rinv is simply Dinv=R and Rinv=D. See page 415 of the text. E. Mathematical representation of the inverse function: how to find it. If possible, write down y=f(x), and solve for x in terms of y. For consistent notation, it is possible to exchange x and y when finished so that you again have something that looks like y f 1 (x). See the steps outlined on page 416. F. Graph of an inverse function is found by reflecting the graph of f about the line y=x. II. The Calculus of Inverse Functions A. If f is a 1:1, continuous function defined on an interval, then its inverse function y f 1 (x) is also continuous. This is a theorem found on page 417 and is used as a condition needed for the existence of the derivative of an inverse function. B. Theorem about differentiability of the inverse function: the function f must have the properties, 1) f is 1:1, 2) f is differentiable. Having checked for this, and giving its inverse the following notation; d 1 xa ) g(x) 1 g(x) | (see f (x) , then at some point a , xa ' dx f (g(x) | page 418 of the text, Theorem 7. Here is an example why it is important that the function be 1:1....Let f (x) x 2 , x . Note that the function is not 1:1 on this interval. But we will pretend not to notice this. Find d f 1 (x) | dx g(x) f 1 (x) d 1 d f (2) dx x2 . By the theorem, we have f '(x) 2x and x . So, we have that 1 dx f 1 (x) | x2 1 1 f '(g(a)) 2x |x g (a ) 2 2 and this does not exist (we cannot take the square root of a negative number