Pre-Calc Homework Solutions 88

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online