Pre-Calc Homework Solutions 442

Pre-Calc Homework Solutions 442 - 442 Cumulative Review 12...

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Unformatted text preview: 442 Cumulative Review 12 1 1 20. y f (1) 1 21. y 2(1 2 h2 h h) 2h 1 h (1 h h)2 2h h2 1 1 9. (a) 2(1) (b) 2 1 19. y 2x tan 3x 1 x x2 1 x2 3 (c) 1 [from (a) and (b)] (d) Yes, since lim f (x) (e) No. Left-hand derivative: lim h0 x1 4 x e e xx (x 3 3x 4 )e x csc x sin x 3 2 (1 csc x 1 cos x cos x)( csc x cot x) (1 cos x)2 f (1 h) h f (1) lim h0 3 csc 2 x (1 (1 cos x)4 (1 (1 3 csc2 x (1 cos x)4 3 csc2 x (1 cos x)4 csc x cot x cot x csc x csc 2 x cos x csc x cot x) cot 2 x) cot x csc x 2 cot 2 x) cot 2 x) lim h0 lim h0 csc 2 x lim h0 h 0 3 csc2 x (csc 2 x (1 cos x)4 3 (sin x)(1 cos x)4 2 cot x csc x 1 (1 Right-hand derivative: lim h0 cos x 2 cos2 x sin2 x cos x)(1 2 cos x) sin 2 x f (1 h) h f (1) lim h0 2 h h (1 h h) 1 3 (sin 2 x)(1 cos x)4 3(1 2 cos x) (sin 4 x)(1 cos x)3 lim h0 1 Since the left- and right-hand derivatives are not equal, f is not differentiable at x 1. 10. Solve 4 x2 0: all x 2 and x , 2x 2 22. y d dx 2 1 1 sin x 2 1 x 1 x2 d dx 2 tan 1 x 2. x 0, x 1 (2 x) 1 11. Horizontal: since as x 1 cos x Vertical: solve 2x 2 x while 0. 1 . 2 1, the end behavior at both ends is y 0 to find x 3 23. d [cos (xy) dx y2 y) ln x] 2yy d (0) dx 1 x ,x x 2 2 y 24. y sin (xy)(xy 1 x 0 12. One possible function is y 3 8 , x y sin (xy) 2y 1 2 x sin (xy) 1 d x 1/2 x 2 dx dy/dt dx/dt 1 xy sin (xy) 2xy x 2 sin (xy) x x x 1 x 2x 1 y x x [ 10, 10] by [ 4, 4] 25. 4 1 5 3 (x 2)2 1/2 dy dx cos t sin t cot t 13. f (5) 5 f (0) 0 (x 2)(1) (x 9 5 (x 2)2 26. ln y ln y 1 dy y dx dy dx ln[(cos x)x] x ln (cos x) x y 1 ( sin x) cos x 14. y 1)(1) 15. y 3 sin 2 sin ( 1 1 1 3x 3x 2 1 3x) (1 2 ln cos x 3x) ( 3) x sin x cos x x sin x x (cos x) ln (cos x) cos x ln (cos x) 16. y sin x sec x (sin x)(1 cos 2 x) cos 2 x tan x cos x sin x cos 2 x (cos x)x sin x 1 [cos x ln (cos x) x sin x] 27. By the Fundamental theorem of Calculus, y 1 x 3. x2 17. y 18. y 1 x 2 2 1 x (2x) 1) 2x x 2 1 28. y 1)e x 2 cos t 2x cos (x 2) 2 sin (2x) cos (2x); (e x )(2x (2x x y 2x sin (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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