Pre-Calc Homework Solutions 322

Pre-Calc Homework Solutions 322 - 322 Section 8.1 x cos x...

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48. Use the intersect function on a graphing calculator to determine that the curves intersect at x 56 1.8933. A shell has radius x and height 3 1 2 x 2 2 } x 2 1 2 0 3 } . The volume, which is calculated using the right half of the area, is E 1.8933 0 2 p ( x ) 1 3 1 2 x 2 2 } x 2 1 2 0 3 } 2 dx , which using NINT evaluates to < 9.7717. 49. (a) y 52} 5 4 } ( x 1 2)( x 2 2) 5 5 2 } 5 4 } x 2 (b) Revolve about the line x 5 4, using cylindrical shells. A shell has radius 4 2 x and height 5 2 } 5 4 } x 2 . The total volume is E 2 2 2 2 p (4 2 x ) 1 5 2 } 5 4 } x 2 2 dx 5 10 p E 2 2 2 1 } 1 4 } x 3 2 x 2 2 x 1 4 2 dx 5 10 p 3 } 1 1 6 } x 4 2 } 1 3 } x 3 2 } 1 2 } x 2 1 4 x 4 5 } 32 3 0 } p < 335.1032 in 3 . 50. Since } d d L x } 5 } 1 x } 1 f 9 ( x ) must equal ˇ 1 w 1 w ( w f 9 w ( x w )) w 2 w , 1 1 ( f 9 ( x )) 2 5 } x 1 2 } 1 } 2 x } f 9 ( x ) 1 ( f 9 ( x )) 2 , and f 9 ( x ) 5 } 1 2 } x 2 } 2 1 x } . Then f ( x ) 5 } 1 4 } x 2 2 } 1 2 } ln x 1 C , and the requirement to pass through (1, 1) means that
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