HW1 - R ? d. Is this function of class C 1 ? e. What is the...

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Homework #1 Due: Tuesday, February 2, 2010 1. (2pt) Compute the following integrals: 1 0 ) log( dx x where log(x) denotes the natural logarithm of x , and dx x a 1 1 for a fixed parameter a>1 . What happens for a=1 ? 2. (5pt) Consider the following function: = = 0 0 0 ) log( ) ( , : 2 x x x x x f R R f a. Is this function continuous on R ? b. Does this function have a derivative at every point x in R ? c. Is this function differentiable on
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Unformatted text preview: R ? d. Is this function of class C 1 ? e. What is the largest integer k so that f is of class C k ? 3. (3pt) Consider the following functions: ∫ = → ⎪ ⎩ ⎪ ⎨ ⎧ = ≠ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = → x dt t g x f R R f x x x x g R R g ) ( ) ( , : if , if , 1 sin ) ( , : Prove that f is differentiable but is not of class C 1 . Total: 10 pts...
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This note was uploaded on 05/05/2010 for the course MATH 464 taught by Professor Staff during the Spring '08 term at Maryland.

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