Pre-Calc Homework Solutions 258

Pre-Calc Homework Solutions 258 - 258 Section 6.4 40. (a)...

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Unformatted text preview: 258 Section 6.4 40. (a) Using y x dx x sin x sin u 1 x 2, du x sin x sin x sin 1 1 37. continued (b) sin 1 f 1 (x) log2 x and f (y) 2 y dy 2y C ln 2 1 log2 x 2 ln 2 2 y, we have x x x x d sin 1 x dx dx 1 1 x2 log2 x dx x log2 x x log2 x x log2 x dx 2x dx 1 1 1 x x x x2 1 u 1/2 du 2 (b) C u 1/2 C x2 log2 x dx x log2 x x log2 x x log2 x x log2 x 1 (c) cos (sin 38. (a) Using y 2 1 x) f 2 1 1 (x) tan 1 d log2 x dx dx 1 x dx x ln 2 dx ln 2 1 x C ln 2 x x and f (y) tan y, (c) 2log2 x x y 1 , we have: x tan x tan 1 1 tan x dx x x tan y dy ln sec y C s Section 6.4 Exponential Growth and Decay (pp. 330341) Exploration 1 Slowing Down More Slowly 1. As m increases the velocity of the object represented by the graph slows down more slowly. That is, the y-coordinates of the graphs decrease to 0 more slowly as m increases. (Section 6.2, Example 7) x tan x tan (b) tan 1 1 1 x x x x ln cos y ln cos (tan x C 1 x) dx C x dx x tan x tan 1 1 d tan 1 x dx dx 1 x dx 1 x2 1 u 1 du 2 1 ln u C 2 1 ln (1 x 2) 2 1 ln (1 2 [0, 20] by [0, 120] t u 1 x 2, du 2x dx x tan x tan x tan 1 1 1 x x x 1 2. As we saw in Section 5.1, s(t) 0 v(u) du gives the C x ) 2 distance traveled by the object over the time interval [0, t]. 0 Since s(0) 0 v(u) du 0, the integral gives the distance (c) ln cos (tan 39. (a) Using y f ( y) cos 1 1 x) 1 ln 1 x2 traveled by the object at time t. 3. The total distance traveled is about 200 units for m 1, about 400 units for m 2, about 800 units for m 4, and about 1200 units for m 6. f (x) x x cos x cos x cos cos 1 x and cos x, 0 x dx , we have: 1 1 1 x x x x x cos y dy sin y sin (cos C 1 x) C [0, 70] by [0, 1500] (b) cos 1 x dx x cos x cos 1 1 d x cos 1 x dx dx 1 Quick Review 6.4 1. a 2. c eb ln d 3) 3 x 2 e2 e2 x 1 x2 dx u 1 x cos x cos x cos x 2, du 1 1 1 2x dx 1 u 1/2 du 2 x x x x) 3. ln (x x 4. 100e e2x 2x x 2x u1/2 1 1 C x2 x2 C 3 (c) sin (cos 1 600 6 ln 6 1 ln 6 2 ...
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