Pre-Calc Homework Solutions 324

Pre-Calc Homework Solutions 324 - 324 Section 8.1 1 sin t 1...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 324 Section 8.1 1 sin t 1 t t sin t . t sin t 1 7. The limit leads to the indeterminate form 1 . Let ln f (x) ln(e x x x0 12. Let f (t) t ln(e x x) x)1/x ex ex 1 x ln(e x x x) . 1 x 2 1 100 0.1884 10 10 2 10 3 lim lim x0 1 ex x x0 e lim 2 f (t) 0.0167 0.0017 0.00017 lim (e x x0 x)1/x lim f (x) x0 lim e ln f (x) x0 e2 Estimate the limit to be 0. lim 1 t0 sin t 1 t lim t0 t lim t0 lim [0, 5] by [0, 10] t0 sin t t sin t 1 cos t t cos t sin t sin t t sin t cos t cos t 0 13. Let f (x) The graph supports the answer. x 8. lim x (1 10 x)1/x. 102 103 104 105 3x 2x x3 x 1 2 lim x 4x 3x 2 3 1 lim x 4 6x 0 f (x) 1.2710 1.0472 1.0069 1.0009 1.0001 Estimate the limit to be 1. ln (1 x) 1 x 1 x ln (1 x) lim lim 1 x x x ln f (x) [ 5, 25] by [ 1, 2] 0 1 x 0 e0 1 The graph supports the answer. 9. (a) x 10 102 103 104 105 lim (1 x x)1/x lim f (x) x lim e ln f (x) 14. Let f (x) x x 2x2 . 3x2 5x f (x) 1.1513 0.2303 0.0345 0.00461 0.00058 10 0.5429 102 0.6525 103 0.6652 104 0.6665 105 0.6667 Estimate the limit to be 0. (b) lim 10. (a) ln x 5 x x 5 ln x x x lim 5/x 1 x lim 10 0 1 f (x) 0 3 x 100 10 1 2 10 10 4 Estimate the limit to be x 2x 2 2 5x x 3x f (x) 0.1585 0.1666 0.1667 0.1667 0.1667 Estimate the limit to be . (b) lim x0 lim 2 . 3 1 4x lim lim 5 x x 6x 2 4 6 2 . 3 1 6 15. lim 0 sin 2 lim sin cos 2 2 cos 1 0 (2)(0) cos (0)2 0 x sin x x3 lim x0 1 lim x0 lim x0 cos x 3x 2 sin x 6x cos x 6 16. lim 1 /2 1 1 6 11. Let f ( ) sin 3 . sin 4 cos 2 sin 2 sin lim /2 4 cos 2 sin /2 4 cos 1 4 /2 lim 17. lim 10 f( ) 0 10 1 10 2 10 3 10 4 t t0 e cos t t 1 1 lim t t0 e sin t 1 lim t0 c os t et 1 0.1865 0.7589 0.7501 0.7500 0.7500 3 4 Estimate the limit to be . lim sin 3 0 sin 4 lim 3 cos 3 0 4 cos 4 3 4 ...
View Full Document

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.

Ask a homework question - tutors are online