2 3 points sketch a vector pointing in the direction

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2. (3 points) Sketch a vector pointing in the direction of f ( P ) in the picture above.
Math 230 Test 2 Fall Quarter 2013 Page 4 of 9 Question 3. (14 points) A bug is whirling upwards along the path r ( t ) = h sin ( t ) , cos ( t ) , t 2 i a. (8 points) Find the curvature of this path at the point (0 , 1 , 0) . b. (6 points) What is the tangential component of acceleration of the bug at the time t = π/ 2 ?
Math 230 Test 2 Fall Quarter 2013 Page 5 of 9 Question 4. (12 points) Find the following limits or show that they do not exist. Regardless of whether the limit does or does not exist show all your work! a. (6 points) lim b. (6 points) lim ( x,y ) (0 , 0)
Math 230 Test 2 Fall Quarter 2013 Page 6 of 9 Question 5. (14 points) Consider the surface x 2 + y 4 + z 4 + 3 xyz = 0 . a. (8 points) Find ∂z ∂x and ∂z ∂y for the function z which is defined implicitly by this equation. b. (6 points) Find the tangent plane to the surface at the point (2 , - 1 , 1)
Math 230 Test 2 Fall Quarter 2013 Page 7 of 9 Question 6. (12 points) Wile E. Coyote looks down and realizes he is walking on a sheet of ice with thickness given by the function T ( x, y ) = x 2 y - sin( y ) . a. (8 points) If Mr. Coyote starts at the point (3 , π ) and walks towards the point (0 , π ) , find the rate of change of thickness of the ice in the direction he travels. b. (4 points) In which direction should Mr. Coyote go if he wants to maximize the rate at which the thickness increases?

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