# Past Exam for MATH 135 - Calculus for Busn/Social Sci with Weber at Christopher Newport (CNU)

## Exam Information

 Material Type: Exam 2 Professor: Weber Class: MATH 135 - Calculus for Busn/Social Sci Subject: Mathematics University: Christopher Newport University Term: Fall 2008

## Sample Document Text

Final 21C Winter 2002 1. (9) Compute f y where f (x,y) = xy e 2 x sin(!y) 3 . 2. a. (8) Suppose you know at some point that ! f ! x = 2, ! f ! y = -3, ! x ! s = -5, ! x ! t = 5, ! y ! s = 4, ! y ! t = -2. What is the value of ! f ! t ? b. (8) Suppose in addition that you know ! s ! u = 2, ! t ! u = 3, what is the value of ! f ! u ? 3. (13) Change the order of integration for the following integral and evaluate. 2 4 # # 1 1 + y 2 dy dx. 0 2x 4. (12) Write the following integral in spherical coordinates. DO NOT EVALUATE 2 p 1 r # # # r dz dr d . 2 q 0 0 r 2 5. (12) Find the critical points of f(x,y) = 6xy 2 - 2x - 3y + 1 3 4 6. (13) Given that (0,0) and (0,4) are critical points for z = 4y + 12yx - 24x - 24 y , 3 2 ...