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e2 - M421 Exam 2 Monday Nov 13 NAME 1 2 3 4 TOTAL The value...

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M421 Exam 2 Monday Nov. 13 NAME: 1 2 3 4 TOTAL The value of each question is indicated next to the question. No calculators, books, or notes are permitted. Except where indicated otherwise, you may use any Theorem we have proved in this class, or any theorem from differential calculus (Mean value theorem, Rolle’s theorem, L’Hopital’s rule, etc). You may not quote results from HW – i.e. you may not say “ As proved in my HW3 we know that ...” Show your work to receive partial credit. If you need extra space, write on the back of the page. No hitting, biting, or fighting.
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1) (10pts) Let f : R n mapsto→ R m . (a) State the definition for f to be differentiable at vectorx = vectora. (b) State what you must show to prove that f is not continuous at vectorx = vectora.
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2) (10pts) (a) State the definition for a sequence
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