Assignment 3 Solutions

Assignment 3 Solutions - MAT 1330, Fall 2010 Assignment 3...

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MAT 1330, Fall 2010 Assignment 3 Due Wednesday October 13, at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Frithjof Lutscher Angelika Welte Aziz Khanchi Robert Smith? DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Question 1. Find a and b such that the function given by f ( x )= a sin( x )+ bx 0 x 2 + a 0 <x 1 b cos(2 πx ax > 1 is continuous. Answer: a = 1 and b = 1 Justify your answer: lim x 0 + x 2 + a = a = lim x 0 - a sin( x b = b .So a = b and also lim x 1 + b cos(2 a = a + b = lim x 1 - x 2 + a =1+ a . Therefore b =1 1

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Question 2. Give an example of a function which is continuous everywhere but not diFerentiable at x = 2. ±or example f ( x )= ( x 2) 2 if x< 2, ( x 2) if x 2. The derivative is given by f ± ( x ± 2( x 2) if 2, 1 if x> 2.
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This note was uploaded on 09/17/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Fall '08 term at University of Ottawa.

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Assignment 3 Solutions - MAT 1330, Fall 2010 Assignment 3...

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