Pre-Calc Homework Solutions 356

Pre-Calc Homework Solutions 356 - 356 Chapter 8 Review 1 1...

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Unformatted text preview: 356 Chapter 8 Review 1 1 1 ln x ln x x 1 (x 1) ln x 1 ln x x x ln x 1 x/x ln x 1 2 f (x) g(x) x x 1/x 1 1/x 2 9. lim x1 x lim x1 17. lim x lim x lim x 1 1 1 x lim x 1 x1 x x1 x f grows at the same rate as g. 18. lim f (x) x g(x) x/100 x x xe lim lim 1 1 ex x 100 lim f grows faster than g. 19. lim x x x1 1 lim f (x) g(x) 1 lim x x tan 2 1 x x since lim tan 10. The limit leads to the indeterminate form 1 x x 0 x and lim x . f grows faster than g. f (x) x g(x) csc 1 x 1/x x f (x) 1 20. lim lim 1 ln f (x) x ln 1 1 x ln (1 1/x) 1/x 1/x 2 1 1/x x lim x x2 1 x2 1 lim x0 ln (1 1/x) 1/x 1 x x lim x0 1/x 2 lim x0 x x 1 0 lim x x x2 1 x2 x2 1 1 1 1/x 2 lim 1 x0 lim eln f (x) x0 e0 1 0 lim x lim 11. The limit leads to the indeterminate form 0 . f( ) ln f ( ) (tan ) ln (tan ) ln (tan ) 1/ sec2 tan 1 2 1 x f grows at the same rate as g. 21. lim f (x) x g(x) xln x log x x x 2 lim lim x ln x x log2x (ln x)/ln 2 1/ln 2) 1) lim x0 ln (tan ) 1/ lim x0 lim xln x x 2 lim x (ln x)(1 x lim x0 sin cos 2 lim x 1 (ln x)(1/ln 2 lim x0 sin2 ln f ( ) cos2 0 Note that 1 x 1 ln 2 0 1. 0 since ln 2 f grows slower than g. lim (tan ) x0 lim e x0 e 0 1 22. lim cos t lim 2t t0 6x 1 1 3x 2 12. lim 2 sin 1 sin t lim 2 t0 t 1 3 1 2 3x 2 4x x f (x) x g(x) 3 x 2 x x lim 2x x x 3 lim lim x 2 x 3 0 since 2 3 1. f grows slower than g. 6x 4 6 12x 2 13. lim 14. lim 15. lim x x 3 3x 2 2 x x 2x 3x 2 x 4 x3 x x f (x) g(x) lim lim x 6 23. lim x f (x) g(x) lim x ln 2x ln x 2 lim x ln x ln 2 2 ln x lim x 1/x 2/x 1 2 6x 3 x 4x lim lim x 6x 0 f grows at the same rate as g. 24. lim f (x) x g(x) lim x x 5x 1 5 lim x 10x 3 ex 2x 2 lim x f grows at the same rate as g. 16. lim f (x) x g(x) lim x lim x log2 x log3 x lim x (ln x)/(ln 2) (ln x)/(ln 3) ln 3 ln 2 lim x 30x2 4x ex 60x 4 ex 60 0 ex f grows at the same rate as g. f grows slower than g. ...
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