EVNREV03 - Review Exercises for Chapter 3 50. Let f x Then...

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Review Exercises for Chapter 3 Review Exercises for Chapter 3 437 50. Let Then tan 0.05 < tan 0 1 sec 2 0 s 0.05 d 5 0 1 1 s 0.05 d . f s 0.05 d < f s 0 d 1 f 9 s 0 d dx f s x d 5 tan x , x 5 0, dx 5 0.05, f s x d 5 sec 2 x . 52. Propagated error relative error and the percent error 5 | dy y | 3 100. 5 | dy y | , 5 f s x 1D x d 2 f s x d , 54. True, D y D x 5 dy dx 5 a 56. False Let Then and Thus, in this example. dy > D y dy 5 f s x d dx 5 1 2 ! 1 s 3 d 5 3 2 . D y 5 f s x x d 2 f s x d 5 f s 4 d 2 f s 1 d 5 1 f s x d 5 ! x , x 5 1, and D x 5 dx 5 3. 2. (a) (c) At least six critical numbers on s 2 6, 6 d . x 4 6 6 4 6 4 2 4 6 y f s 4 d 52 f s 2 4 d 3 (b) (d) Yes. Since and the Mean Value says that there exists at least one value c in such that (e) No, exists because f is continuous at (f) Yes, f is differentiable at x 5 2. s 0, 0 d . lim x 0 f s x d f s c d 5 f s 1 d 2 f s 2 2 d 1 2 s 2 2 d 5 2 2 2 1 1 1 2 1. s 2 2, 1 d f s 1 d f s 2 1 d 2, f s 2 2 d f s 2 d s 2 1 d 5 1 f s 2 3 d f s 3 d s 2 4 d 5 4 4. No critical numbers Left endpoint: Minimum Right endpoint: Maximum s 2, 2 y ! 5 d s 0, 0 d 5 1 s x 2 1 1 d 3 y 2 f s x d 5 x 3 2 1 2 s x 2 1 1 d 2 3 y 2 s 2 x d 4 1 s x 2 1 1 d 2 1 y 2 f s x d 5 x ! x 2 1 1 , ± 0, 2 g 6. No. f is not differentiable at x 5 2. 8. No; the function is discontinuous at which is in the interval ± 2 2, 1 g . x 5 0 10. c 5 2 f s c d 5 2 1 c 2 1 4 f s b d 2 f s a d b 2 a 5 s 1 y 4 d 2 1 4 2 1 5 2 3 y 4 3 1 4 f s x d 1 x 2 f s x d 5 1 x , 1 x 4 12. c 5 1 f s c d 5 1 2 ! c 2 2 3 2 f s b d 2 f s a d b 2 a 5 2 6 2 0 4 2 0 3 2 f s x d 5 1 2 ! x 2 2 f s x d 5 ! x 2 2 x , 0 x 4
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438 Chapter 3 Applications of Differentiation 16. Critical number: x 52 1 g 9 s x d 5 3 s x 1 1 d 2 g s x d 5 s x 1 1 d 3 Interval Sign of Conclusion Increasing Increasing g s x d > 0 g s x d > 0 g s x d 2 1 < x < ` 2 ` < x < 2 1 14. c 5 2 5 Midpoint of ± 0, 4 g f s c d 5 4 c 2 3 5 5 f s b d 2 f s a d b 2 a 5 21 2 1 4 2 0 5 5 f s x d 5 4 x 2 3 f s x d 5 2 x 2 2 3 x 1 1 18. Critical numbers: x 5 p 4 , x 5 5 4 f s x d 5 cos x 2 sin x f s x d 5 sin x 1 cos x , 0 x 2 Interval Sign of Conclusion Increasing Decreasing Increasing f s x d > 0 f s x d < 0 f s x d > 0 f s x d 5 4 < x < 2 4 < x < 5 4 0 < x < 4 20. Relative maximum: Relative minimum: 1 3 1 2 , 2 3 2 ² 1 1 1 2 , 3 2 ² 5 0 when x 5 1 1 2 , 3 1 2 g s x d 5 3 2 1 2 ² cos 1 x 2 2 1 ² g s x d 5 3 2 sin 1 x 2 2 1 ² , ± 0, 4 g Test Interval Sign of Conclusion Increasing Decreasing Increasing g s x d > 0 g s x d < 0 g s x d > 0 g s x d 3 1 2 < x < 4 1 1 2 < x < 3 1 2 0 < x < 1 1 2 22. (a) Therefore, When y 5 A 1 A ! A 2 1 B 2 ² 1 B 1 B ! A 2 1 B 2 ² 5 ! A 2 1 B 2 . v 5 y 5 0, cos s ! k y m t d 5 B ! A 2 1 B 2 . sin s ! k y m t d 5 A ! A 2 1 B 2 5 0 when sin ! k y m t cos ! k y m t 5 A B tan s ! k y m t d 5 A B . y 5 A ! k y m cos s ! k y m t d 2 B ! k y m sin s ! k y m t d y 5 A sin s ! k y m t d 1 B cos s ! k y m t d (b) Period: Frequency: 1 2 y !
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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EVNREV03 - Review Exercises for Chapter 3 50. Let f x Then...

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