Pre-Calc Homework Solutions 174

Pre-Calc Homework Solutions 174 - 174 Section 4.5 r 2h, we...

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46. Since V 5 p r 2 h , we have } d d V r } 5 2 p rh , and dV 5 2 p rh dr . We want ) dV ) # 0.001 V , which gives ) 2 p rh dr ) # 0.001 p r 2 h , or ) dr ) # 0.0005 r . The variation of the radius should not exceed } 20 1 00 } of the ideal radius, that is, 0.05% of the ideal radius. 47. We have } d d W g }52 bg 2 2 , so dW 52 bg 2 2 dg . Then } d d W W m ea o r o th n } 5 } 2 2 b b ( ( 5 3 . 2 2 ) ) 2 2 2 2 d d g g }5} 5 3 . 2 2 2 2 } < 37.87. The ratio is about 37.87 to 1. 48. (a) Note that T 5 2 p L 1/2 g 2 1/2 , so } d d T g p L 1/2 g 2 3/2 and dT p L 1/2 g 2 3/2 dg . (b) Note that dT and dg have opposite signs. Thus, if g increases, T decreases and the clock speeds up. (c) 2 p L 1/2 g 2 3/2 dg 5 dT 2 p (100) 1/2 (980) 2 3/2 dg 5 0.001 dg < 2 0.9765 Since dg < 2 0.9765, g < 980 2 0.9765 5 979.0235. 49. If f 9 ( x ) ± 0, we have x 2 5 x 1 2 } f f 9 ( ( x x 1 1 ) ) } 5 x 1 2 } f 9 ( 0 x 1 ) } 5 x 1 . Therefore x 2 5 x 1 , and all later approximations are also equal to x 1 . 50. If x 1 5 h , then f 9 ( x 1 ) 5 } 2 h 1 1/2 } and x 2 5 h 2 5 h 2 2 h h . If x 1 h , then f 9 ( x 1 ) 52} 2 ˇ 1 h w } and x 2 h 25 2 h 1 2 h 5 h [ 2 3, 3] by [ 2 0.5, 2] 51. Note that f 9 ( x ) 5 } 1 3 } x 2 2/3 and so x n 1 1 5 x n 2 } f f 9 ( ( x x n n ) ) } 5
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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