Unformatted text preview: centered at 0 for f ( x ) = sin x only involve odd powers of x , so we have T 1 ( x ) = T 2 ( x ), T 3 ( x ) = T 4 ( x ) and so on, and so the picture shows only four curves alongside the graph of f ( x ) = sin x . Now let f ( x ) = 2 x + 1 √ 4x 2 , and complete the following problems. Problem 1: Use MAPLE to list the ﬁrst 5 Taylor polynomials T 1 ( x ) , T 2 ( x ) , ··· , T 5 ( x ) centered at 0 for the function f ( x ) = 2 x +1 √ 4x 2 . Problem 2: Use MAPLE to plot the graphs of each of these 5 Taylor polynomials alongside the graph of f ( x ) = 2 x +1 √ 4x 2 in the viewing rectangle2 ≤ x ≤ 2,5 ≤ y ≤ 5. Problem 3: Use MAPLE to estimate the maximum value of ﬂ ﬂ f ( x )T 5 ( x ) ﬂ ﬂ for 0 ≤ x ≤ 1 (one way to do this is to plot the function f ( x )T 5 ( x ) in a suitable viewing rectangle). 1...
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 Winter '07
 Anoymous
 Calculus, Polynomials, Derivative, Taylor Polynomials

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