Pre-Calc Homework Solutions 123

Pre-Calc Homework Solutions 123 - Chapter 3 Review dy dt dx...

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52. } d d y x } 55 } 1 2 1 si c n os t t } At t 52} p 4 } , we have x 5 cos 1 2} p 4 } 2 5 } ˇ 2 2 w } , y p 4 } 1 sin 1 2} p 4 } 2 p 4 } 2 } ˇ 2 2 w } , and } d d y x } 5 ˇ 2 w 1 1. The equation of the tangent line is y 5 ( ˇ 2 w 1 1) 1 x 2 } ˇ 2 2 w } 2 2 } p 4 } 2 } ˇ 2 2 w } , or y 5 (1 1 ˇ 2 w ) x 2 ˇ 2 w 2 1 2 } p 4 } . This is approximately y 5 2.414 x 2 3.200. 53. (a) [ 2 1, 3] by 3 2 1, } 5 3 } 4 (b) Yes, because both of the one-sided limits as x 1 are equal to f (1) 5 1. (c) No, because the left-hand derivative at x 5 1 is 1 1 and the right-hand derivative at x 5 1 is 2 1. 54. (a) The function is continuous for all values of m , because the right-hand limit as x 0 is equal to f (0) 5 0 for any value of m . (b) The left-hand derivative at x 5 0 is 2 cos (2 ? 0) 5 2, and the right-hand derivative at x 5 0 is m , so in order for the function to be differentiable at x 5 0, m must be 2. 55. (a) For all x ± 0 (b) At x 5 0 (c) Nowhere 56. (a) For all x (b) Nowhere (c) Nowhere 57. Note that lim x 0 2 f ( x ) 5 lim x 0 2 (2 x 2 3) 52 3 and lim x 0 1 f ( x ) 5 lim x 0 1 ( x 2 3) 3. Since these values agree with f (0), the function is continuous at x 5 0. On the other hand, f 9 ( x ) 5 5 , so the derivative is undefined at x 5 0. (a) [ 2 1, 0) < (0, 4] (b) At x 5 0 (c) Nowhere in its domain 58. Note that the function is undefined at x 5 0. (a) [ 2 2, 0) < (0, 2] (b) Nowhere (c) Nowhere in its domain
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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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