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Pre-Calc Homework Solutions 171

# Pre-Calc Homework Solutions 171 - Section 4.5 13 Center(x...

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13. Center 5 1 f 9 ( x ) 5 } ( x 1 1 ( x )( 1 1) 1 2 ) 2 ( x )(1) } 5 } ( x 1 1 1) 2 } We have f (1) 5 } 1 2 } and f 9 (1) 5 } 1 4 } L ( x ) 5 f (1) 1 f 9 (1)( x 2 1) 5 } 1 2 } 1 } 1 4 } ( x 2 1) 5 } 1 4 } x 1 } 1 4 } Alternate solution: Using center 5 } 3 2 } , we have f 1 } 3 2 } 2 5 } 3 5 } and f 9 1 } 3 2 } 2 5 } 2 4 5 } . L ( x ) 5 f 1 } 3 2 } 2 1 f 9 1 } 3 2 } 21 x 2 } 3 2 } 2 5 } 3 5 } 1 } 2 4 5 } 1 x 2 } 3 2 } 2 5 } 2 4 5 } x 1 } 2 9 5 } 14. Center 5 } p 2 } f 9 ( x ) 5 2 sin x We have f 1 } p 2 } 2 5 0 and f 9 1 } p 2 } 2 5 2 1. L ( x ) 5 f 1 } p 2 } 2 1 f 9 1 } p 2 } 21 x 2 } p 2 } 2 5 0 2 1 1 x 2 } p 2 } 2 5 2 x 1 } p 2 } 15. Let f ( x ) 5 x 3 1 x 2 1. Then f 9 ( x ) 5 3 x 2 1 1 and x n 1 1 5 x n 2 } f f 9 ( ( x x n n ) ) } 5 x n 2 } x n 3 3 x 1 n 2 x 1 n 2 1 1 } . Note that f is cubic and f 9 is always positive, so there is exactly one solution. We choose x 1 5 0. x 1 5 0 x 2 5 1 x 3 5 0.75 x 4 < 0.6860465 x 5 < 0.6823396 x 6 < 0.6823278 x 7 < 0.6823278 Solution: x < 0.682328 16. Let f ( x ) 5 x 4 1 x 2 3. Then f 9 ( x ) 5 4 x 3 1 1 and x n 1 1 5 x n 2 } f f 9 ( ( x x n n ) ) } 5 x n 2 } x n 4 4 x 1 n 3 x 1 n 2 1 3 } The graph of y 5 f ( x ) shows that f ( x ) 5 0 has two solutions.
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