318midterm 2.pdf

# 318midterm 2.pdf - Math 318 Midterm 2 Mar 31 2017 Read the...

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Math 318 Midterm 2 Mar. 31, 2017 Read the questions carefully and answer them in the spaces provided. Show necessary work for your answer. During your reasoning, you may use any theorems from the textbook or the lecture. But you need to state what the theorems said clearly. Name 1. Let U R n be an open set. Give the formal definition of a function f : U R m being continuous at point a in U . 1

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2. Prove that if f : R n R m is differentiable at point a , then f is continuous at point a . Page 2
3. Find an equation of a tangent plane to the surface defined by 1 2 x 2 + xy + 3 yz 2 = 7 at the point (2 , 1 , 1). Page 3

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