Multivariable Calculus Test 1 2008 | MATH 2224, Exams of Calculus

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MATH 2224: Test 1 (11/22/2008) Show all work and reasoning! The correct answer alone does not guarantee any points. 1. Determine the line of intersection of the planes given by the equations w-Qy=1 and 2e+y+2z=2. 2. Sketch the surface given by the equation 2? + y+ z* = 1. Clearly show shape, position and orientation. 3. Sketch the level curves for the function f(x,y) = zy for the function values g=-4,z=-1,2=0,z=landz=4. 4, Show that the following limit does not exist: 2. lim 2. feu)(0.0) 2 + yf! 5, Determine the lst and 2nd order partial derivatives of the function f(x,y) = sin ey. 6. Let y¥ zoo) Pew, your, Use the chain rule to calculate 2B, The answer should be expressed in u and v only (no x or y). Simplify your answer as far as possible, No points are given if you do not use the chain rule. 7. Compute the directional derivative of the function f(x,y) = 2°y — 2y? at the point P (2,1) in the direction of the vector v = 4i ~ 3j.