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quiz2_all - Quiz 2 MA 225 B2 Spring 2011 Instructor...

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Quiz 2 – MA 225 B2 – Spring 2011 Instructor: Margaret Beck TF: Man-Ho Ho Date: March 9, 2011 Name: BU ID: Score: 1. (out of 20) 2. (out of 20) 3. (out of 45) 4. (out of 15) Total: (out of 100) Instructions: Please write clearly and show all work. No credit will be given if answers are not justified. If the problem asks you to use a specific method in your solution, please make sure you do so. No credit will be given if another method is used. The point value of each problem is written in bold at the beginning of each problem.
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Question 1 [20 points] Determine whether or not the following limit exists. If it exists, what is its value? (Make sure you justify your answer.) lim ( x,y ) (0 , 0) 5 x 3 y x 4 + 3 y 4 Question 2. [20 points] Suppose that g ( x, y ) = x 2 cos( x + y ) , x = 3 t , y = te t . Find dg dt when t = 3.
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Question 3. [45 points] Consider the function f ( x, y ) = 2 xy + x 2 . (i) Find the directional derivative of f in the direction of the vector 1 , 2 . (ii) Find the equation of the tangent plane to the surface defined by the equation z = f ( x, y ) at the point (1 , 1 , 3).
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(iii) Find the critical points of f and determine whether they are local maxima, minima, or saddles. Question 4 [15 points] The dimensions of a rectangle are 10cm and 20cm, with an error in measure- ment of at most 3cm. Use di ff erentials to calculate the maximum error in computing the area of the rectangle.
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