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05aut-m2

# 05aut-m2 - MATH 51 MIDTERM II Name Numeric Student ID...

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MATH 51 MIDTERM II November 17, 2005 Name: Numeric Student ID: Instructor’s Name: I agree to abide by the terms of the honor code: Signature: Instructions: Print your name, student ID number and instructor’s name in the space provided. During the test you may not use notes, books or calculators. Read each question carefully and show all your work ; full credit cannot be obtained without sufficient justification for your answer unless explicitly stated otherwise. Underline your final answer to each question. There are 9 questions. You have 90 minutes to do all the problems. Question Score Maximum 1 10 2 6 3 8 4 6 5 10 6 10 7 15 8 10 9 10 Total 85

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Question 5 of 9, Page 2 of 4 Solutions 1. Consider the function f ( x, y ) = x 4 y 3 and the point P = (1 , 1 , 1) on its graph. (a) Write down the equation of the tangent plane at the graph of the function at the point P . (b) Using your answer from (a), write down an expression for the change, Δ z , in z = f ( x, y ) depending on Δ x and Δ y , the change in x and y , respectively, near the point P = (1 , 1 , 1). Is the function
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