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9-2&3_Practice - Math 604 AP Calculus BC Name Part...

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1 Math 604 – AP Calculus BC Name_____________________________ Part III – Taylor & Maclaurin Polynomial Practice Maclaurin Series at x = 0 : f ( x ) ! f (0) + " f (0) x + "" f (0) 2! x 2 + + f ( n ) (0) n ! x n + = f ( k ) (0) k ! x k k = 0 # $ Use the table of Maclaurin series. Construct the first three nonzero terms and the general term of the Maclaurin series generated by the function, and give the interval of convergence. 1. f ( x ) = sin 2 x 2. f ( x ) = tan ! 1 x 2 3. f ( x ) = e ! 2 x
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2 Taylor Series at x = a : f ( x ) ! f ( a ) + " f ( a )( x # a ) + "" f ( a ) 2! ( x # a ) 2 + + f ( n ) ( a ) n ! ( x # a ) n + = f ( k ) ( a ) k ! ( x # a ) k k = 0 $ % Find the Taylor Polynomials of order 3 centered at the given points. 4. f ( x ) = 1 x + 1 ; x = 2 5. f ( x ) = e x 2 ; x = 1
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3 6. Let f be a function that has derivatives of all orders for all real numbers. Assume that f (1) = 4 ! f
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9-2&3_Practice - Math 604 AP Calculus BC Name Part...

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