Math 121 - Exam 2-11/17/2014 Name: Section: Section Class,Times Day Instructor Section Class,Times Day Instructor 1 09:00%AM%(%09:50%AM M%T%W%%F% Li,%Huilan 15 11:00%AM%(%11:50%AM M%T%W%%F% Perlstadt,%Marci 2 09:00%AM%(%09:50%AM M%T%W%%F% Lee,%Hwan%Yong 16 04:00%PM%(%04:50%PM M%T%W%%F% Aran,%Jason 3 09:00%AM%(%09:50%AM M%T%W%%F% Papadopoulos,%Dimitrios 21 12:00%PM%(%01:50%PM M%%W%%% White,%Richard 5 02:00%PM%(%02:50%PM M%T%W%%F% Swartz,%Kenneth 22 02:00%PM%(%02:50%PM M%T%W%%F% Grinshpan,%Anatolii 6 09:00%AM%(%09:50%AM M%T%W%%F% Grinshpan,%Anatolii 23 01:00%PM%(%01:50%PM M%T%W%%F% Papadopoulos,%Dimitrios 7 10:00%AM%(%10:50%AM M%T%W%%F% Li,%Huilan 24 01:00%PM%(%01:50%PM M%T%W%%F% Perline,%Ronald 8 10:00%AM%(%10:50%AM M%T%W%%F% Perlstadt,%Marci 25 05:00%PM%(%05:50%PM M%T%W%%F% Aran,%Jason 9 12:00%PM%(%12:50%PM M%T%W%%F% Papadopoulos,%Dimitrios 26 11:00%AM%(%11:50%AM M%T%W%%F% Lee,%Hwan%Yong 11 01:00%PM%(%01:50%PM M%T%W%%F% Aran,%Jason 27 12:00%PM%(%12:50%PM M%T%W%%F% Zhang,%Aijun The following rules apply: This is a closed-book exam. You may not use any books or notes on this exam. For free response questions, you must show all work. Answers without proper justification will not receive full credit. Partial credit will be awarded for significant progress towards the correct answer. Cross off any work that you do not want graded. For multiple choice questions, circle the letter of the best answer. Make sure your circles include just one letter. These problems will be marked as correct or incorrect; partial credit will not be awarded for problems in this section. You have 50 minutes to complete this exam. When time is called, stop writing immediately and turn in your exam to the nearest proctor. You may not use any electronic devices including (but not limited to) calculators, cell phone, or ipods. Using such a device will be considered a violation of the university s academic integrity policy and, at the very least, will result in a grade of 0 for this exam. Page Points Score 2 15 3 15 4 15 5 15 6 10 7 10 8 10 9 10 Total: 100 For word problems, all answers must include the appropriate units in order to earn full credit.
Math 121 Exam 2 - Page 2 of 9 11/17/2014 Part I: Free Response 1. (15 points) Find an equation of the tangent line to the curve x 2 xy + y 2 = 3 at the point (1, 1).
Math 121 Exam 2 - Page 3 of 9 11/17/2014 2. (15 points) Oil spilled from a ruptured tanker spreads out in a circle whose area increases at a constant rate of 6 square miles per hour. How fast is the radius of the spill increasing at the instant when the area is 9π square miles? Your answer should include appropriate units.
Math 121 Exam 2 - Page 4 of 9 11/17/2014 3. (15 points) Evaluate the following limit. If the limit does not exist, write +,, or DNE, whichever is most appropriate. ( 4 lim x 0 + x 4 ) e x 1
Math 121 Exam 2 - Page 5 of 9 11/17/2014 4. (15 points) At which value(s) of x will the tangent line to f(x) = ln (x 2 + 4) be parallel to y = 1 2 x 1 5?
Math 121 Exam 2 - Page 6 of 9 11/17/2014 Part II: Multiple Choice 5. (5 points) If y = cos 2 3x, then dy dx = (a) 6 sin 3x cos 3x (b) 2 cos 3x (c) (d) (e) 2 cos 3x 6 cos 3x 2 sin 3x cos 3x 6. (5 points) If y = 3 x, then d2 y dx 2 = (a) 3 x (b) 3 x (ln 3) 2 (c) (3 x ln 3) 2 (d) 3 x 1 + 3 x ln 3 (e) x(x 1)3 x 2 + 3 x 1
Math 121 Exam 2 - Page 7 of 9 11/17/2014 ( x ) 7. (5 points) An equation of the tangent line to the graph of y = arcsin at the origin is 2 (a) x = 0 (b) y = 0 (c) x y = 0 (d) x 2y = 0 (e) πx 2y = 0 8. (5 points) If f(x) = (x 2 2x 1) 2/3, then f (0) is (a) 4 3 (b) 0 (c) 2 3 (d) 4 3 (e) 2
Math 121 Exam 2 - Page 8 of 9 11/17/2014 9. (5 points) Evaluate lim x 1 x 2 4 x + 1 (a) 4 (b) 3 2 (c) 1 (d) 5 4 (e) 2 2 10. (5 points) Evaluate lim + 1) tan x x 0 +(x (a) 1 (b) e (c) e 2 (d) π 2 (e) π 4
Math 121 Exam 2 - Page 9 of 9 11/17/2014 11. (5 points) Using the local linear approximation of f(x) = 4 + x at x 0 = 0, approximate the value of f(0.12). (a) 1.98 (b) 2.00 (c) 2.03 (d) 2.06 (e) 2.12 12. (5 points) Suppose 0 < x < π 2. If y = (sin x)x, then dy dx = (a) x ln x(sin x) (b) (sin x) x cos x (c) x(sin x) x 1 (cos x) (d) (sin x) x (x cos x + sin x) (e) (sin x) x (x cot x + ln (sin x))