hw02-sol - Homework # 2 Due: 5/30/06 1. Use the graph to...

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Unformatted text preview: Homework # 2 Due: 5/30/06 1. Use the graph to find the following limits: lim x 2 + f ( x ) lim x 2- f ( x ) lim x 2 f ( x ) lim x f ( x ) lim x - 1 f ( x ) 2. Sketch the graph of a function that satisfies all of the given conditions: lim x - f ( x ) = 1 lim x + f ( x ) = 2 f (0) = 1 lim x 1 f ( x ) = 1 f ( x ) is undefined 3. Use the limit laws to find the following limits. Justify each step. (a) lim x - 3 ( x 2 + 3)( x- 4) lim x - 3 ( x 2 + 3)( x- 4) = lim x - 3 ( x 2 + 3) lim x - 3 ( x- 4) Law 4 = lim x - 3 x 2 + lim x - 3 3 lim x - 3 x- lim x - 3 4 Laws 1 and 2 = lim x - 3 x 2 + 3 lim x - 3 x- 4 Law 7 = ( (- 3) 2 + 3 ) (- 3- 4) Law 9 =- 84 (b) lim x 2 x- 2 x 3- 8 First, x- 2 x 3- 8 = 1 x 2 +2 x +4 lim x 2 1 x 2 + 2 x + 4 = lim x 2 1 lim x 2 ( x 2 + 2 x + 4) Law 5 = lim x 2 1 lim x 2 x 2 + lim x 2 2 x + lim x 2 4 Laws 1,2 = lim x 2 1 lim x 2 x 2 + 2 lim x 2 x + lim x 2 4 Law 3 =...
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This note was uploaded on 02/29/2008 for the course MAT 141 taught by Professor Varies during the Spring '08 term at Lehigh University .

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hw02-sol - Homework # 2 Due: 5/30/06 1. Use the graph to...

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