Pre-Calc Homework Solutions 219

Pre-Calc Homework Solutions 219 - Section 5.4 Exploration 2...

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Unformatted text preview: Section 5.4 Exploration 2 x 219 The Effect of Changing a in 10. f (t) dt a dy dx 1 dx/dy 1 3x Section 5.4 Exercises 3 1. 1. 2 1/2 1 dx x 3 2x ln x 1/2 [ 4.7, 4.7] by [ 3.1, 3.1] (6 5 5 5 ln 3) ln 3 ln 3 ln 6 1 2 1 ln 1 2 ln 1 2 2. ln 2 3.208 [ 4.7, 4.7] by [ 3.1, 3.1] 3. Since NINT(x 2, x, 0, 0) 4. Since NINT(x , x, 5, 5) 2 0, the x-intercept is 0. 0, the x-intercept is 5. d dx x 1 2. 2 3x dx 1 3x ln 3 1 1 ln 3 3 26 3 ln 3 5. Changing a has no effect on the graph of y It will always be the same as the graph of y x f (t) dt. a 9 7.889 f (x). 1 6. Changing a shifts the graph of y a f (t) dt vertically in 3. 0 5 (x 2 x 3/2 dx 6/5 x) dx 2 5/2 x 5 5 0 such a way that a is always the x-intercept. If we change a 1 3 x 3 2 3/2 x 3 1 0 1 3 2 3 (0 5 5 2 0) 22.361 1 from a1 to a2, the distance of the vertical shift is 1 f (t) dt. 4. 0 a 2 (25 5 1/5 32 5 0) 1 2 1 1 2 10 2 32 Quick Review 5.4 1. dy dx 5. 1 x 1 dx 2 2 5x 1 5 1 1 cos(x 2) 2x 2(sin x)(cos x) 2x cos (x 2) 6. 2 sin x cos x 2(tan x)(sec2 x) 0 7. 0 dy 2. dx 2 2 dx x2 x 2 dx 2 x 21 1 2 1 3. dy dx 2(sec x)(sec x tan x) 2 sec2 x tan x sin x dx (1 0 cos x 0 1 x sin x ( 1) 2 2 tan x sec2 x 8. cos x) dx ( 0 4. 5. dy dx dy dx 3 3x 7 7x 0 0) 3.142 (0 0) 2x ln 2 /3 dy 6. dx 1 1/2 x 2 1 2 x x sin x cos x x2 9. 0 2 sec2 /3 d 2 tan 0 2( 2 5 /6 3 3 cot 0) 3.464 5 /6 7. 8. dy dx dy dt dy dx ( sin x)(x) (cos x)(1) x2 cos t, dy/dt dx/dt dx dt sin t cos t sin t 10. cot t /6 csc2 d /6 3 2 3 /4 ( 3 3) 3.464 3 /4 9. Implicitly differentiate: dy x dx dy (x dx dy dx (1)y 2y) y x 1 2y 1 (y dy 2y dx 1) 1 x 11. /4 /3 csc x cot x dx 4 sec x tan x dx 0 csc x /4 /3 ( 4(2 0 2) 1) ( 4 2) 0 y 2y 12. 4 sec x ...
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