Pre-Calc Homework Solutions 173

Pre-Calc Homework Solutions 173 - Section 4.5 r 2 and dA dr...

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38. (a) Note that A 5 p r 2 and } d d A r } 5 2 p r , so dA 5 2 p r dr . When r changes from a to a 1 dr , the change in area is approximately 2 p a dr . Substituting 2 for a and 0.02 for dr , the change in area is approximately 2 p (2)(0.02) 5 0.08 p < 0.2513 (b) } d A A } 5 } 0. 4 0 p 8 p } 5 0.02 5 2% 39. Let A 5 cross section area, C 5 circumference, and D 5 diameter. Then D 5 } C p } , so } d d D C } 5 } p 1 } and dD 5 } p 1 } dC . Also, A 5 p 1 } D 2 } 2 2 5 p 1 } 2 C p } 2 2 5 } 4 C p 2 } , so } d d C A } 5 } 2 C p } and dA 5 } 2 C p } dC . When C increases from 10 p in. to 10 p 1 2 in. the diameter increases by dD 5 } p 1 } (2) 5 } p 2 } < 0.6366 in. and the area increases by approximately dA 5 } 1 2 0 p p } (2) 5 10 in 2 . 40. Let x 5 edge length and V 5 volume. Then V 5 x 3 , and so dV 5 3 x 2 dx . With x 5 10 cm and dx 5 0.01 x 5 0.1 cm, we have V 5 10 3 5 1000 cm 3 and dV 5 3(10) 2 (0.1) 5 30 cm 3 , so the percentage error in the volume measurement is approximately } d V V } 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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