Practice Midterm 2 Solutions

Math 125a practice exam 2 page 4 of 8 1 for x 2 let

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Unformatted text preview: on [0, 1]. Math 125A Practice Exam 2 Page 4 of 8 1 for x ∈ [2, ∞). Let f (x) = 0 for 1 + nx x ∈ [2, ∞). Using the definition, prove {fn } converges uniformly to f on x ∈ [2, ∞). 4. ( pts ) Let the sequence of functions {fn } be fn (x) = Math 125A Practice Exam 2 Page 5 of 8 5. ( pts ) For x ∈ [0, 1], we have the following power series √ 1+x= ￿ Use this fact to build a power series for √ (−1)n (2n)! xn . 2 (4n ) (1 − 2n)(n!) 1 1 − x2 6. ( pts ) Prove the following series converges uniformly on R to a continuous function ∞ ￿1 cos nx n2 n=1 M...
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This document was uploaded on 02/27/2014 for the course MATH 125A at UC Davis.

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