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Unformatted text preview: 126 Chapter 3 Review
200 e5 74. continued (c) One possible answer: If the current ridership is less than 40, then the proposed plan may be good. If the current ridership is greater than or equal to 40, then the plan is not a good idea. Look at the graph of y r(x). 78. (a) P(0) 1 1 student
200 e5 200 1
1 (b) lim P(t)
t lim
t 1 t 200 students (c) P (t) d 200(1 dt e 5 t) 200(1
200e 5 t (1 e 5 t)2 (1 e 5 t) 2(e 5 t)( 1) [0, 60] by [ 50, 200] 75. (a) Since x
dx dt tan , we have
d dt P (t) e5 t)2(200e5 t)( 1) (200e5 t)(2)(1 (1 e5 t)4 e 5 t)( 200e 5 t) 400(e 5 t)2 (1 e 5 t)3 e5 t)(e5 t)( 1) (sec 2 )
dx 0 and dt 0.6 sec 2 . At point A, we have 0.6 sec 0
2 (1 0.6 km/sec. (b) 0.6 rad sec 1 revolution 2 rad 60 sec 18 = revolutions per 1 min (200e 5 t)(e 5 t 1) (1 e 5 t)3 minute or approximately 5.73 revolutions per minute. 76. Let f(x) f (x) sin (x cos (x sin x). Then sin x) (x
d dx Since P occurs at t 0 when t 5, the critical point of y P (t) 5. To confirm that this corresponds to the 0 for t 5 sin x) maximum value of P (t), note that P (t) and P (t) t 0 for t cos (x cos (x cos x sin x)(1 sin x) cos x). This derivative is zero when 5. The maximum rate occurs at 0 (which we need not solve) or when 2k for integers k. For each sin (2k f (x) sin 2k ) 0 for x 2k , 79. 5, and this rate is
200e 0 (1 e 0)2 200 22 1,which occurs at x f(2k ) P (5) 50 students per day. of these values, f(x) sin (2k 0) Note: This problem can also be solved graphically. 0. Thus, f(x) which means that the graph has a horizontal tangent at each of these values of x.
d 1 dr 2rl d 1 dl 2rl d 1 dd 2rl 1 T d 2 d 1 dT 2rl 1 1 d 2 T T d T d T d
3/2 77. y (r) y (l) y (d)
1 2rl y (T)
1 2rl T d 4rl 1 T d 1 1 2l d dr r 2r 2l 1 T d 1 1 2r d dl l 2rl 2 1 T d (d 1/2) 2rl dd T 1 d3 4rl 1 1 d ( T) 2rl d dT 1 dT T d T d [ , ] by [ 4, 4] k , where k is an odd integer
4 2 2 (a) x (b) , (c) Where it's not defined, at x (d) It has period
2 k , k an odd integer
4 and continues to repeat the pattern seen in this window. Since y (r) 0, y (l) 0, and y (d) 0, increasing r, l, or 0, d would decrease the frequency. Since y (T) increasing T would increase the frequency. ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.
 Fall '08
 GERMAN

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