Pre-Calc Homework Solutions 78

Pre-Calc Homework Solutions 78 - 78 Section 3.3 dy dx d 1 4...

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Unformatted text preview: 78 Section 3.3 dy dx d 1 4 x dx 4 d (3) dx d 1 3 x dx 3 d 1 2 x dx 2 d (x 1) dx 1 2 x 1 2 x 10. ( x 1) ( x 1) 18. 4 4 dy dx d dx ( x 1) x x 1 1 ( x 1)2 1) 2 ( x 2 1) 2 x x d 2y dx 2 5 5 x x x x 3 3 x x 2 2 0 1 1)2 x( x 1)2 2 x( x d (x 3) dx 3 x( x d ( x 5) dx 6 d (x 4) dx d (x 2) dx 5x 11. (a) dy dx 4x 5 3x 4 2x 19. dy dx (x 2 d (x dx (x 3x 3x 2 1)(x 1)(x 2) 2) d x2 dx x 2 3x 3x 2)(2x 5x 2 2 3) 6) d [(x 1)(x 2 1)] dx d (x 1) (x 2 1) (x 2 dx d 1) (x dx 1) (2x 3 2)(2x 3) (x 2 3x (x 2 3x 2)2 5x 6) (2x 3 3x 2 (x 2 3x 2)2 (x 2x 2 3x 2 dy (b) dx 1)(2x) 2x 2x x2 1 (x 2 1)(1) 1 12 6x 2 (x 2 3x 2)2 20. (a) Let f (x) d [(x dx d 3 (x dx x. f (x) lim h0 1)(x x2 x 1 2 1)] 1) d (x) dx h0 h f (x h) h f (x) lim h0 (x h) h x 3x 2 lim h lim (1) h0 1 2x (b) Note that u 12. (a) dy dx 3 d x x dx x (x 2 d dx 2 u(x) is a function of x. lim h0 3) (x 2 x2 3) (x) d dx d ( u) dx u(x h) h h) h h) [ u(x)] h u(x) lim h0 u(x u(x x(2x) (x 2 x2 lim 3) h0 u(x) du dx d (c) dx 21. x 2 3 x2 d d (c f (x)) c f (x) f (x) dx dx d d c f (x) 0 c f (x) dx dx f (x) 0 1 d f (x) dx (b) dy dx d x2 3 x dx 3 1 x2 d (x dx 3x 1 ) 1 3x 2 d 1 22. dx f (x) [ f (x)]2 f (x) [ f (x)]2 This is equivalent to the answer in part (a). dy 13. dx dy 14. dx d 2x dx 3x d dx x2 2 23. (a) At x 0, d (uv) dx u(0)v (0) 13 v(0)u (0) (5)(2) 5 2 5x x2 (3x 2)(2) (3x (2x 2)2 5)(3) (3x 19 2)2 ( 1)( 3) 1 3 0 15. dy dx 5x 2x d (1 5x 1 dx 5 2 x2 x3 1) (b) At x x 2 ) v(0)u (0) u(0)v (0) d u [v(0)]2 dx v ( 1)( 3) (5)(2) 7 ( 1)2 0, d (x dx d (1 dx 1)(x 2 x x3 3 x ) 0 (1 3x 4 d x3 1 dx x3 3 x4 x)(2x) (c) At x 0, d v dx u ( 1)( 3) (5)2 d (7v dx u(0)v (0) v(0)u (0) [u(0)]2 7 25 (5)(2) 16. dy dx d 1 x dx 1 x 2 x 2 2x 1 (1 x 2)2 d x2 dx 1 x 3 x 2)( 1) (1 (1 x 2)2 (d) At x 7(2) 0, 2u) 20 7v (0) 2u (0) 2( 3) 17. dy dx (1 x 3)(2x) x 2( 3x 2) (1 x 3)2 x 4 2x (1 x 3)2 ...
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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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