Pre-Calc Homework Solutions 326

Pre-Calc Homework Solutions 326 - 326 Section 8.1 2x x 1 26...

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Unformatted text preview: 326 Section 8.1 2x x 1 26. lim (ln 2x x ln (x 2x x 1 1)) lim ln x 33. The limit leads to the indeterminate form Let f (x) ln (ln x)1/x ln (ln x) lim x x 0 . Let f (x) lim x . 2 (ln x)1/x. ln (ln x) x 2x x 1 2 x 1 lim Therefore, lim (ln 2x x lim x 1/x ln x ln (x ln sin x) x . sin x 1)) lim ln f (x) x ln 2 1 lim x 1 x ln x 0 27. lim (ln x x0 lim ln x0 x sin x lim (ln x)1/x x lim eln f (x) x e0 1 0 Let f (x) x lim x0 sin x 34. The limit leads to the indeterminate form 1 Let f (x) ln (1 (1 2x) 1/(2 ln x) . 1 lim x0 cos x . Therefore, lim (ln x x0 2x)1/(2 ln x) lim x ln sin x) 1 x lim ln f (x) x0 ln 1 0 ln (1 2x) lim 2 ln x x ln (1 2x) 2 ln x 2 1 2 x x 2x 28. lim x0 1 x lim x0 1 x x lim x x 1 2x lim x 1 2 1 2 29. The limit leads to the indeterminate form 1 . Let f (x) (e x x)1/x. lim (1 x 2x)1/(2 ln x) lim eln f (x) e1/2 e 35. The limit leads to the indeterminate form 00. Let f (x) x) ln (e lim x0 x x) x 1/x ln (e x x (x 2 2x 2x 1)x 1 1)x (x 1 ln (x 2 1 x 1) ln (x 2 2x 1 x 2x 1 2 2x 1 (x 1 1)2 2x 1) ln (e x) x lim x0 ex ex 1 2 e2 0 ln (x 2 1) lim (e x x0 x)1/x lim e ln f (x) x0 30. The limit leads to the indeterminate form Let f (x) 1 x ln 2 x 1 x2 1 x . 1 x . x2 1 x ln 2 x 2/x 3 1/x 2 2 lim ln (x 2x 1 x 1 1) lim x1 x2 x1 ln 1 x2 1 x 2(x 1) (x 1)2 lim 1 x1 (x 1)2 ln lim lim 2x x0 2(x ln f (x) 1) e 0 0 1 lim x0 lim x0 1/x 2 0 x1 lim (x x1 2 2x 1) x 1 lim e x1 1 x x2 x0 lim lim e ln f (x) x0 e0 3 4x 1 1 0 7 11 36. The limit leads to the indeterminate form 00. Let f (x) (cos x)cos x. (cos x) ln (cos x) sin x 31. lim x 3x 2x 2 sin 7x x 5 2 lim x ln (cos x)cos x ln (cos x) sec x 32. lim x0 tan 11x 2 x0 11 sec 11x lim 7 cos 7x ln (cos x) cos x lim sec x x /2 x /2 sec x tan x lim x /2 sec x tan x lim lim tan x cos x 0 e0 1 x /2 lim (cos x)cos x x /2 lim e ln f (x) x /2 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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