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9-2_Polynomials

# 9-2_Polynomials - f x = x 3 2 x 2 3 x 5 and show that it is...

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1 Math 604 – AP Calculus BC Name_____________________________ 9.2 Taylor & Maclaurin Polynomials 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 # \$ Find the Maclaurin Polynomials of order 4 for f ( x ) and use it to approximate f (0.25) . 1. f ( x ) = e 2 x 2. f ( x ) = sin2 x 3. f ( x ) = ln( x + 1) 4. f ( x ) = tan ! 1 x

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2 Taylor Series at x = a : f ( x ) ! f ( a ) + " f ( a ) x + " 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 x = a for the given function. 5. f ( x ) = e x ; x = 2 6. f ( x ) = tan x ; x = ! 4 7. f ( x ) = tan ! 1 x ; x = 1
3 8. Find the Taylor Polynomial of order 3 centered at 2 for
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Unformatted text preview: f ( x ) = x 3 ! 2 x 2 + 3 x + 5 and show that it is an exact representation of f ( x ) . 9. Find the Maclaurin Polynomial of order n for f ( x ) = 1 (1 ! x ) . Then use it with n = 4 to approximate each of the following. (a) f (0.1) (b) f (0.5) (c) f (0.9) (d) f (2) How does this example show you that the Maclaurin series can be exceedingly poor if x is far from zero?...
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