Pre-Calc Homework Solutions 328

# Pre-Calc Homework Solutions 328 - 328 Section 8.1(b Part(a...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 328 Section 8.1 (b) Part (a) shows that as the number of compoundings per year increases toward infinity, the limit of interest compounded k times per year is interest compounded continuously. 50. (a) For x lim 0, f (x) g (x) 1 1 46. Answers may vary. (a) f (x) 3x 1; g(x) lim x x 1 f (x) lim x g(x) 3x x lim x 2 3 1 3 1. (b) f (x) x 1; g(x) lim x x 1 f (x ) f (x) lim x g(x) x x2 1 lim x 2x 0 x0 g (x) 1 2 1 f (x) lim x0 g (x) 2 (c) f (x) lim x x 2; g(x) f (x) g(x) x x x 2 1 1 lim x lim x 2x 1 (b) This does not contradict L'Hpital's Rule since lim f (x) 2 and lim g (x) 1. x0 t x0 51. (a) A(t) 0 e x dx e x t e 0 t 1 lim ( e t t 47. Find c such that lim f (x) lim f (x) x0 c. 1) lim t t lim x0 9x lim x0 lim x0 lim x0 3 sin 3x 5x3 9 9 cos 3x 15x2 27 sin 3x 30x 81 cos 3x 81 30 30 x0 lim A(t) 1 et t 1 1 (b) V(t) 0 (e x)2 dx e 2x 27 10 t 0 dx Thus, c 27 . This works since lim f (x) 10 x0 c f (0), so f is continuous. 48. f (x) is defined at x form 0 . ln x x x ln x ln x 1 x 1 x 1 x2 0 1 2x t e 2 0 1 2t e 2 2 V(t) lim t A (t) 1 2 0. lim f (x) leads to the indeterminate x0 ( e 2t 1) ( e e 2t t lim t 2 1) 1 2 (1) 1 2 ln x lim x0 1 x x lim x0 lim x0 x 1 0 (c) lim V(t) t0 A (t) ( e lim 2 t0 2t t 1) 1 e lim x x0 lim e x0 x ln x e 0 lim 2 0. Extend the t0 (2e e t 2t ) Thus, f has a removable discontinuity at x definition of f by letting f (0) 1. 2 (2) 1 49. (a) The limit leads to the indeterminate form 1 . Let f (k) ln f (k) r kt . k r kt ln 1 k 1 52. (a) t ln 1 1 k r k x 0.1 0.01 0.001 f (x) 0.04542 0.00495 0.00050 0.00005 t ln 1 lim k r k t 1 k lim k r r 1 k2 k 1 k2 1 0.0001 The limit appears to be 0. (b) lim x0 1 lim k rt 1 r k rt 1 r kt k rt r kt k sin x 2x 0 1 0 L'Hpital's Rule is not applied here because the limit is A0 lim 1 k k lim A0 1 not of the form limit 1. 0 or 0 , since the denominator has A0 lim e ln f (k) k A0 e rt ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online