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Pre-Calc Homework Solutions 379

# Pre-Calc Homework Solutions 379 - Section 9.3 379 19 f(0...

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19. f (0) 5 ln (cos x ) ) x 5 0 5 ln 1 5 0 f 9 (0) 5 } co 1 s x } ( 2 sin x ) ) x 5 0 5 2 tan x ) x 5 0 5 0 f 0 (0) 5 2 sec 2 x ) x 5 0 5 2 1 so } f 0 2 ( ! 0) } 5 2 } 1 2 } (a) L ( x ) 5 0 (b) P 2 ( x ) 5 2 } 1 2 } x 2 (c) The graphs of the linear and quadratic approximations fit the graph of the function near x 5 0. [ 2 3, 3] by [ 2 3, 1] 20. f (0) 5 e sin x ) x 5 0 5 e 0 5 1 f 9 (0) 5 e sin x cos x ) x 5 0 5 1 f 0 (0) 5 3 ( e sin x )( 2 sin x ) 1 (cos x )( e sin x cos x ) 4 ) x 5 0 5 1, so } f 0 2 ( ! 0) } 5 } 1 2 } (a) L ( x ) 5 1 1 x (b) P 2 ( x ) 5 1 1 x 1 } x 2 2 } (c) The graphs of the linear and quadratic approximations fit the graph of the function near x 5 0. [ 2 3, 3] by [ 2 1, 3] 21. f (0) 5 (1 2 x 2 ) 2 1/2 ) x 5 0 5 1 f 9 (0) 5 2 } 1 2 } (1 2 x 2 ) 2 3/2 ( 2 2 x ) ) x 5 0 5 x (1 2 x 2 ) 2 3/2 ) x 5 0 5 0 f 0 (0) 5 ( x ) 3 2 } 3 2 } (1 2 x 2 ) 2 5/2 ( 2 2 x ) 4 1 (1 2 x 2 ) 2 3/2 ) x 5 0 5 1, so } f 0 2 ( ! 0) } 5 } 1 2 } (a) L ( x ) 5 1 (b) P 2 ( x ) 5 1 1 } x 2 2 } (c) The graphs of the linear and quadratic approximations fit the graph of the function near x 5 0. [ 2 3, 3] by [ 2 1, 3] 22. f (0) 5 sec x ) x 5 0 5 1 f 9 (0) 5 sec x tan x ) x 5 0 5 0 f 0 (0) 5 (sec x )(sec 2 x ) 1 (tan x )(sec x tan x ) ) x 5 0 5 1, so } f 0 2 ( !
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