Math 3A, Fall 2010 Exam 2 NAME: ________________________________________________________ PLEASE PRINT Check your discussion section: ___ 1A Tue Sherwood ___ 1C Tue Farzin ___ 1E Tue Charles ___ 1B Thur Sherwood ___ 1D Thur Farzin ___ 1F Thur Charles You have 50 minutes to complete this exam. No notes, books, or calculators are allowed. Show all work. Unsupported or illegible answers will receive no credit. There are a total of 50 points on this exam. You may use the differentiation formulas below. 21212111tan11cos11sinxxdxdxxdxdxxdxd+=−−=−=−−− 21212111cot11sec11cscxxdxdxxxdxdxxxdxd+−=−=−−=−−− PAGE SCORE POINTS 1 8 2 12 3 10 4 10 5 10 TOTAL 501.) [4 points] Sketch a continuous function h(x) that satisfies the following properties: existnot does )3( 3for x 0)( ,0)( 3for x 0)( ,0)(hxhxhxhxh′>>′′<′<<′′>′ 2.) [4 points] Consider the function xxexf3)(−=. a.) Specify the intervals on which f(x) is increasing and decreasing. b.) Specify the intervals on which f(x) is concave up and concave down.3.) [12 points] Differentiate the functions below using logarithmic differentiation. a.) 312)14(csc)(+=−xxexfx b.) ()xxxgsec253)( +=4.) [10 points] Evaluate the limit. Show all work. a.) 20)cos()cos(limxnxmxx−+→ where m,n are constants b.) xxxtan0lim+→5.) [10 points] Einstein's Theory of Relatives states that the more time you spend with your relatives at Thanksgiving, the more times you will hear the awful question: "So what are you planning to do after graduation?" If you spend T hours with your relatives, the number of times N you will be asked the question is given by: 143+= TN A Math 3A student estimates that she will spend 3 hours with her relatives, give or take 10 minutes. What is the error in her prediction of the number of times she will be asked the awful question?6.) [10 points] The dwarves of Moria need to construct a large open-top box with a square base to hold a captured troll. The box needs to have a volume of 100 m3. To hold the angry troll, the sides of the box need to be constructed with a sturdier material than the base. Gimli calculates that the base will cost $3 per square meter to construct, but the sides will cost $5 per square meter. What dimensions should the dwarves use to construct the minimum cost box? Include units in your final answer. To receive full credit, you must justify that your answer is a