Solution a): The total surface area of cone is rL r 2 . Now, rL r 2 9. Also, 2 r b b r . 2 So, rL r 2 9 2 b b L 9 2 2 bL b 2 9 2 4 2 bL b 2 9 4 2 bL b 2 36 2 bL 36 b 2 36 b 2 18 b 2 b b 2 Domain of L(b) is all real numbers such that b 0. L Solution b): 36 b 2 18 b 2 b b 2 18 1 L '(b) 2 2 b 18 1 L '(b) 0 2 0 2 b 18 1 2 2 b 2 b 2 18 L(b) b 18. Hence, L(b) has an absolute minimum at b 18. Solution c): h L2 (b / 2) 2 2 18 18 2 ( 18 / 2) . 2 18 18 18 . 2 18 Total amount of material used in tent flaps 2 L 2 Math 2250: Calculus I For Science And Engineering Fall 2015, Dr. Klipper Paper Homework 8: Due THURSDAY, October 29, 2015 by 5pm (You may slip your assignment under my oce door or put it in my faculty mailbox.) Write up solutions to the following problems with all detail shown. Present your work well! Style and clarity will be part of your grade. (See the syllabus for more detail about grade breakdowns.) You are allowed to show me early drafts of your work and get suggestions. 1. (similar to WeBWorK Section 4.5 #14): In this problem, we will compute the limit of the following 00 indeterminate form: lim ln(x)x1 x1+ (a) First, say y = ln(x)x1 and u = ln(y). Rewrite u in some way where L'Hpital's Rule can be used. With each step, indicate which kind of indeterminate form you have as x 1+ . (b) Use L'Hpital's Rule on your answer from part (a) to nd the limit of u as x 1+ . (c) Finally, what is the limit of y as x 1+ ? 2. (based on WeBWorK Section 4.6): The opening of a tent (pictured below) consists of two diagonal aps of length L, standing up from the ground. When the tent is properly constructed, the opening forms an isosceles triangle, where the base is b feet wide. The total area of the tent opening is 9 square feet. We want to build this opening to use as little material as possible. (a) Express L as a function of b alone. What is the domain of this function L(b)? (b) Find the value of b where L(b) attains its absolute minimum. Explain carefully why you know you have the absolute minimum. (c) With the value of b you found in part (b), gure out the height of the tallest point of the tent and the total amount of material used in the tent aps