Pre-Calc Homework Solutions 106

Pre-Calc Homework Solutions 106 - 106 31. Section 3.7 6x 2...

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Unformatted text preview: 106 31. Section 3.7 6x 2 d (6x 2) dx d (3xy) dx dy 12x 3x dx dy 3x dx 3xy 2y 2 17y 6 0 34. x sin 2y y cos 2x d (x sin 2y) dx d (y cos 2x) dx d d d (17y) (6) (0) dx dx dx dy dy (3y)(1) 4y 17 0 0 dx dx dy dy 4y 17 12x 3y dx dx dy (3x 4y 17) 12x 3y dx dy 12x 3y dx 3x 4y 17 12( 1) 3(0) 3( 1) 4(0) 17 6 (x 7 7 (x 6 12 14 6 x 7 6 7 6 7 7 x 6 7 6 d (2y 2) dx (x)(cos 2y)(2) dy dx (sin 2y)(1) (cos 2x) dy dx dy (cos 2x) dx dy dx (y)( sin 2x)(2) (2x cos 2y) dy dx 2y sin 2x 2y sin 2x 2x cos 2y sin ( ) cos 2 sin 2y sin 2y cos 2x Slope at ( 1, 0): (a) Tangent: y (b) Normal: y 32. d 2 (x ) dx 2 Slope at 1) 1) 3xy 0 or y 0 or y 2y 2 4 2 , : 0 0 2 4 sin 2 2 cos ( ) ( )(1) 2 ( 1) 2 x2 d 3 (xy) dx 5 d (5) dx (a) Tangent: y (b) Normal: y 2x 2x 4y 2x 1 2 4 2 or y or y 2x 1 x 2 5 8 2x dy 3(x) dx d 2 (y 2) dx dy 3(y)(1) 4y dx dy ( x 3 4y) dx dy dx 2 3 3 3 2 3 4(2) x y 0 y y 4 2 3 3 x 3 35. 2 sin ( x d 2 sin ( x dx y) y) y) y) dy dx Slope at ( 3, 2): (a) Tangent: y (b) Normal: x 33. 2xy d 2 (xy) dx 0 [1 2 cos ( x 2 3 sin y d (sin y) dx dy cos y dx dy cos y) dx dy dx dy dx dy dx dy y)] dx dy dx 2 cos 2 cos 2 cos ( x 2 cos ( x 2 cos ( x y) 1 2 cos ( x y) 2 ( 1) 2( 1) 2 d (2 ) dx Slope at (1, 0): (a) Tangent: y (b) Normal: y 2y 2x cos y 1 1 2 2 x x 2 2x dy dx 2 (x 1 (x 2 1) 1) 0 or y 0 or y 2 1 2 2y(1) (2x 0 2y 36. x 2 cos2 y sin y 0 d (0) dx Slope at 1, 2 : 2( /2) 2(1) cos( /2) 2 (a) Tangent: y (b) Normal: y 2 2 (x 1) 1) 2 or y 2 2 x 2 2 d (sin y) dx dy (x 2)(2 cos y)( sin y) dx d 2 (x cos2 y) dx (cos2 y)(2x) dy dx 1 (cos y) dy dx 0 (2x 2 cos y sin y dy dx 2 cos y) 2x cos2 y 2x cos y 2x2 sin y (x 2 or y x cos y 2x cos y 2x 2 cos y sin y 2(0) cos 2(0)2 sin Slope at (0, ): (a) Tangent: y (b) Normal: x 1 0 0 ...
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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.

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