Pre-Calc Homework Solutions 122

Pre-Calc Homework Solutions 122 - 122 45 dy dx Chapter 3...

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Unformatted text preview: 122 45. dy dx Chapter 3 Review d dx x2 2x 2 1 x2 2x (2x 2(3) 2) 3 x x2 1 2x (a) Tangent: y (b) Normal: y dy dt dx dt 5 (x 4 4 (x 5 4) 4) 1 or y 1 or y 4 x 5 5 x 4 11 5 6 At x and dy dx 3, we have y 3 32 1 2(3) 2 3 32 2 3 . 3 or y 3 2 3 (a) Tangent: y (b) Normal: y or y 46. dy dx d (4 dx 3 2 (x 3 (x 2 5 3 2 3) 3) x 3 49. dy dx 2 sin t 2 cos t tan t 2 sin dy dx 3 4 At t y 3 , we have x 4 2, tan 3 4 x 2 cos 3 4 2, and 1. cot x 2 csc x) The equation of the tangent line is y dy dx csc 2 x At x y dy dx 2 2 csc x cot x 1(x dy dt dx dt 2) ( 2), or y 4 cot t 3 x 2 2. , we have 2 2 4 cot csc 2 2 csc 2 csc 1 x 1 x 2 2 4 cot 2 0 2 1 2 and 2(1)(0) x x 1. 2 50. 4 cos t 3 sin t At t y 3 , we have x 4 3 cos dy dx 3 4 3 2 4 3 cot 3 4 2 , 4 . 3 (a) Tangent: y (b) Normal: y 2 2 or y 2 or y 2 4 sin 3 4 2 2, and 2 2 2 The equation of the tangent line is y 4 x 3 dy dt dx dt 47. Use implicit differentiation. x2 d 2 (x ) dx 2y 2 9 d (9) dx 3 2 2 2 2, or y 4 x 3 4 2. d (2y 2) dx dy 2x 4y dx dy dx 0 2x 4y 1 2(2) 1 (x 4 1 4 x 2y dy 51. dx 5 sec 2 t 3 sec t tan t 5 sec t 3 tan t 5 3 sin t At t y 6 , we have x 3 sec 6 2 5 3 sin 3, 10 . 3 6 Slope at (1, 2): (a) Tangent: y (b) Normal: y 1) 1) 2 or y 2 or y 4x 1 x 4 9 4 5 tan 6 5 3 dy , and dx 3 The equation of the tangent line is 4(x 2 y 48. Use implicit differentiation. x d (x) dx d ( dx 10 (x 3 2 3) 5 3 , or y 3 10 x 3 5 3. xy xy) 6 d (6) dx 1 2 1 xy (x) dy dx 2 (y)(1) x dy xy dx dy dx 0 1 2 2 x y 2 x xy y xy y 2 y x 5 4 xy 1 Slope at (4, 1): 2 1 4 1 4 2 2 1 4 ...
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