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Pre-Calc Homework Solutions 88

# Pre-Calc Homework Solutions 88 - 88 Section 3.5 d(4 dx d(4...

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Unformatted text preview: 88 Section 3.5 d (4 dx d (4) dx d dx d dx 6. When the graph of cos x is increasing, the graph of NDER (cos x) is positive (above the x-axis). When the graph of cos x is decreasing, the graph of NDER (cos x) is negative (below the x-axis). When the graph of cos x stops increasing and starts decreasing, the graph of NDER (cos x) crosses the x-axis from above to below. The slope of the graph of cos x matches the value of NDER (cos x) at these points. We conjecture that NDER (cos x) sin x. The graphs coincide, supporting our conjecture. 5. x 2 sin x) x 2 (sin x) (sin x) (x 2) 0 [x 2 cos x x 2 cos x (sin x)(2x)] 2x sin x 6. d (3x dx x tan x) d (3x) dx x (tan x) tan x d dx (tan x) (x) d dx 3 7. d 4 dx cos x x cos x d (4 sec x) dx (1 x sec 2x 4 sec x tan x d dx d 8. dx 1 [ 2 , 2 ] by [ 4, 4] cos x) (x) (1 x d (1 dx 2 cos x) cos x) 1 cos x x sin x (1 cos x)2 cot x) (cot x) (1 2 Quick Review 3.5 1. 135 2. 1.7 3. sin 180 180 3 4 306 3 3 2 2.356 97.403 d cot x 9. dx 1 cot x (1 (1 d dx (cot x) (1 cot x) 2 d dx cot x) cot x)( csc x) (cot x)( csc 2 x) (1 cot x)2 csc2 x (1 cot x)2 csc2 x sin2 x (1 cot x)2 sin2 x (1 sin x) (cos x) (1 (1 d dx 1 (sin x d dx cos x)2 sin x) 4. Domain: All reals Range: [ 1, 1] 5. Domain: x k for odd integers k 2 d cos x 10. dx 1 sin x (cos x) (1 sin x) 2 sin x)( sin x) (cos x)(cos x) (1 sin x)2 sin x sin 2 x cos 2 x (1 sin x)2 Range: All reals 6. cos a 7. If tan a sin a 8. 1 1 2 (1 cos h h sin2 h h(1 cos h) 2 1 sin2 a 3 4 1 ( 1)2 0 0 (1 sin x) (1 sin x)2 1 1 sin x 1, then a . k for some integer k, so cos h)(1 cos h) h(1 cos h) 1 cos 2 h h(1 cos h) 11. y (x) y( ) d (sin x dx 3) 1 cos x cos The tangent line has slope ( , sin 3) ( , 3). 1(x 1 and passes through 9. y (x) 6x 14x y (3) 12 The tangent line has slope 12 and passes through (3, 1), so its equation is y 12(x 3) 1, or y 12x 35. 10. a(t) a(3) v (t) 12 6t 2 14t Its equation is y ) 3, or y x 3. Section 3.5 Exercises 1. 2. 3. 4. d (1 dx x cos x) tan x) 0 1 ( sin x) sec 2 x 1 sin x d (2 sin x dx d 1 dx x 2 cos x 1 x2 5 sin x d dx 5 cos x sec x (x) sec x d dx d (x sec x) dx x (sec x) x sec x tan x ...
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