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hw02-sol

# hw02-sol - Homework 2 Due 1 Use the graph to find the...

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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 0 f ( x ) lim x →- 1 f ( x ) 2. Sketch the graph of a function that satisfies all of the given conditions: lim x 0 - f ( x ) = 1 lim x 0 + 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

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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 = 1 lim x 2 x 2 + 2 lim x 2 x + 4 Law 7 = 1 2 2 + 2(2) + 4 Law 9 = 1 12 Note: I don’t think I intended for the denominator to be x 3 - 8. I think I wanted x 3 - 2.
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hw02-sol - Homework 2 Due 1 Use the graph to find the...

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