Chap2_Sec3

Chap2_Sec3 - USING THE LIMIT LAWS Example 1 (2.3) Use the...

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Use the Limit Laws and the graphs of f and g in the figure to evaluate the following limits, if they exist. a. b. c. [ ] 2 lim ( ) 5 ( ) x f x g x →- + USING THE LIMIT LAWS Example 1 (2.3) [ ] 1 lim ( ) ( ) x f x g x 2 ( ) lim ( ) x f x g x
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Find s Let f ( x ) = ( x 2 - 1)/( x - 1) . s We can’t find the limit by substituting x = 1 because f (1) isn’t defined. s We can’t apply the Quotient Law because the limit of the denominator is 0. s Instead, we need to do some preliminary algebra. 2 1 1 lim . 1 x x x - - USING THE LIMIT LAWS Example 3 (2.3)
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Evaluate s If we define , then, we can’t compute by letting h = 0 since F (0) is undefined. s However, if we simplify F (h) algebraically, we find that: 2 0 (3 ) 9 lim . h h h + - USING THE LIMIT LAWS Example 5 (2.3) 2 (3 ) 9 ( ) h F h h + - = 0 lim ( ) h F h
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s We can’t apply the Quotient Law immediately—since the limit of the denominator is 0. s
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Chap2_Sec3 - USING THE LIMIT LAWS Example 1 (2.3) Use the...

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