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Pre-Calc Homework Solutions 331

# Pre-Calc Homework Solutions 331 - Section 8.2 1 x ln x x 1...

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19. lim x } 1 l / n ˇ x x w } 5 lim x } ˇ x w 1 ln x } 5 0 } ˇ 1 x w } grows slower than ln x as x . 20. lim x } l e n 2 x x } 5 lim x } e x 1 ln x } 5 0 e 2 x grows slower than ln x as x . 21. lim x } x 2 ln 2 x ln x } 5 lim x 1 } ln x x } 2 2 2 5 lim x 1 } 1 1 / x } 2 2 2 5 lim x ( x 2 2) 5 ‘ x 2 2 ln x grows faster than ln x as x . 22. lim x } 5 ln ln x x } 5 5 5 ln x grows at the same rate as ln x as x . 23. Compare e x to x x . lim x } e x x x } 5 lim x 1 } e x } 2 x 5 0 e x grows slower than x x . Compare e x to (ln x ) x . lim x } (ln e x x ) x } 5 lim x 1 } ln e x } 2 x 5 0 e x grows slower than (ln x ) x . Compare e x to e x /2 . lim x } e e x x /2 } 5 lim x e x /2 5 ‘ e x grows faster than e x /2 . Compare x x to (ln x ) x . lim x } (ln x x x ) x } 5 lim x 1 } ln x x } 2 x 5 ‘ since lim x } ln x x } 5 lim x } 1 1 / x } 5 ‘ .
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