Pre-Calc Homework Solutions 332

Pre-Calc Homework Solutions 332 - 332 Section 8.2 2 cos x 2...

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28. Compare f 1 to f 2 . lim x } f f 2 1 ( ( x x ) ) } 5 lim x 5 lim x } x 4 1 x 4 2 1 x 2 x 2 3 1 } 5 lim x 5 1 Thus f 1 and f 2 grow at the same rate. Compare f 1 and f 3 . lim x } f f 3 1 ( ( x x ) ) } 5 lim x 5 lim x } 2 x x 5 5 1 2 x 1 3 } 5 lim x 5 2 Thus f 1 and f 3 grow at the same rate. By transitivity, f 2 and f 3 grow at the same rate, so all three functions grow at the same rate. 29. (a) False, since lim x } x x } 5 1 ± 0. (b) False, since lim x } x 1 x 5 } 5 1 ± 0. (c) True, since lim x } x 1 x 5 } 5 1 # 1. (d) True, since lim x } 2 x x } 5 } 1 2 } # 1. (e) True, since lim x } e e 2 x x } 5 lim x } e 1 x } 5 0. (f) True, since lim x } x 1 x ln x } 5 lim x 5 1 # 1. (g) False, since lim x } l l n n 2 x x } 5 lim x } 1 1 / / x x } 5 1 ± 0. (h) True, since lim x } ˇ x 2 w x 1 w 5 w }5 lim x ! 1
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