Math 125: Exam 2 Wednesday, September 24, 2008 Version A Name: NetID (UT email): @utk.edu Fill in the box for the recitation section you are enrolled in: 12.40 Lauren Sipe Section 7 8.10 Lauren Sipe Section 8 11.10 Jesse Smith Section 9 2.10 Jesse Smith Section 10 3.40 Jesse Smith Section 11 8.10 James LePage Section 12 9.40 Lauren Sipe Section 13 11.10 James LePage Section 14 2.10 James LePage Section 15 3.40 Joshua Smeton Section 16 The Honor Statement An essential feature of the University of Tennessee is a commitment to maintaining an atmosphere of intellectual integrity and academic honesty. As a student of the University, I pledge that I will neither knowingly give nor receive any inappropriate assistance in academic work, thus affirming my own personal commitment to honor and integrity. Signature: Date: No cell phones or PDAs. No iPods. No books, notes, or papers. No TI-83, 84, or 89. No sharing calculators. Keep your eyes on your own paper. Refrain from talking during the exam. If you observe cheating, please bring it to the attention of one of the proctors. Do not open this exam until you are directed to start. Answer every question and show all work. You must show complete and appropriate work to receive full credit. All parts are five points each. You do not need to simplify! Good luck! 1. Use the long way with the limit to find the derivative of f (x) = 2x + 4. For this problem, show all work, and simplify completely. 2. Find f0(x) (a) f (x) = 3x 73 4px + 6x2 (b) f (x) =p16x2 + 9 (c) f (x) = 6x3x2 + x 3. At a hockey game in Wasilla, AK, an obnoxious fan throws a penny on the ice. The height of the penny in feet above the ice t seconds after it is thrown is given by the function h(t). Interpret the meaning of the statement h0(1) = 16. Give your answer as a complete sentence with proper units on all quanties. 4. Let f (x) = 1x. Is f (x) continuous at x = 0? Why or why not? 5. Find f0(x) (a) f (x) = px x2 + x (b) f (x) = 45p8x 6. Let y = x4. Find d 3y dx3 . 7. The number of pounds of moose meat in Sarah Palinâ€™s freezer t days after the end of hunting season is given by the function m(t). Interpret the meaning of the statement m0(30) = 2. Give your answer as a complete sentence with proper units on all quanties. 8. Evaluate lim x!4 f (x), if the limit exists. Let f (x) = ( 10 x if x < 4 2x 2 if x 4 9. Find f0(x) (a) f (x) = (6x7 2x2 + x16)( 4x3 10x8 + 6x7) (b) f (x) = 5x + 2x3 7 10. Let y = (x2 + 5x)2. Find d 2y dx2 . 11. Bristol Palin is undergoing a medical test where her blood glucose levels are being tested t minutes after drinking a glucose solution. The blood glucose level, measured in mmol/l, is given by the function g(t). Interpret the meaning of the statement g0(90) = 0.014. Give your answer as a complete sentence with proper units on all quantities. 12. Find f0(x) (a) f (x) = (2x7 9x + 3)6 (b) f (x) = 13x 34276 (c) f (x) = 110 (d) f (x) = 7px 4 13. Let AC(x) be the average cost function for a t-shirt vendor who sells x Sarah Palin t-shirts, where the average cost is measured in dollars per shirt. If MAC(x) is the marginal average cost function, interpret the statement MAC(100) = 0.25. Give your answer as a complete sentence with proper units on all quantities.