hw2 - M421 HW 2 Due Friday Sept. 21 From Wade Section 5.2...

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Unformatted text preview: M421 HW 2 Due Friday Sept. 21 From Wade Section 5.2 5.3 Page Number 124-125 131-133 Problems 2, 3, 5a, 8 3c, 4abd, 8 Non-book Exercises 1) For n = 1, 2, . . . , define gn (x) = 2xne−nx for x ∈ [0, 1]. (a) Show that ∀x ∈ [0, 1], lim gn (x) = 0. n→∞ 2 (b) Using the Fundamental Theorem of Calculus to evalutate the integrals on the left, show that 1 1 n→∞ 0 lim gn (x)dx = 0 n→∞ lim gn (x) dx. 2) Show that if f ∈ I[a, b] then g(x) ≡ sin(f (x)) ∈ I[a, b]. 1 ...
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This note was uploaded on 07/25/2008 for the course MATH 421 taught by Professor Promislow during the Fall '07 term at Michigan State University.

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