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Pre-Calc Homework Solutions 67

Pre-Calc Homework Solutions 67 - Chapter 2 Review 28 2x 2...

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28. [ 2 4, 4] by [ 2 3, 3] (a) Vertical asymptotes: x 5 0, x 5 2 2 ( b) At x 5 0: Left-hand limit 5 lim x 0 2 } x 2 x ( x 2 1 1 2) } 5 2‘ Right-hand limit 5 lim x 0 1 } x 2 x ( x 2 1 1 2) } 5 2‘ At x 5 2 2: Left-hand limit 5 lim x –2 2 } x 2 x ( x 2 1 1 2) } 5 ‘ Right-hand limit 5 lim x –2 1 } x 2 x ( x 2 1 1 2) } 5 2‘ 29. (a) At x 52 1: Left-hand limit 5 lim x 2 1 2 f ( x ) 5 lim x 2 1 2 (1) 5 1 Right-hand limit 5 lim x 2 1 1 f ( x ) 5 lim x 2 1 1 ( 2 x ) 5 1 At x 5 0: Left-hand limit 5 lim x 0 2 f ( x ) 5 lim x 0 2 ( 2 x ) 5 0 Right-hand limit 5 lim x 0 1 f ( x ) 5 lim x 0 1 ( 2 x ) 5 0 At x 5 1: Left-hand limit 5 lim x 1 2 f ( x ) 5 lim x 1 2 ( 2 x ) 5 2 1 Right-hand limit 5 lim x 1 1 f ( x ) 5 lim x 1 1 (1) 5 1 (b) At x 5 2 1: Yes, the limit is 1. At x 5 0: Yes, the limit is 0. At x 5 1: No, the limit doesn’t exist because the two one-sided limits are different. (c) At x 5 2 1: Continuous because f ( 2 1) 5 the limit. At x 5 0: Discontinuous because f (0) the limit.
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