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# Lab2 - centered at 0 for f x = sin x only involve odd...

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MATH 138 Calculus 2, MAPLE Lab Assignment 2 Due: Monday , March 29 by 11:00 am in the MATH 138 drop boxes outside MC 4066. We can have MAPLE list the first 7 Taylor polynomials T 1 ( x ) , T 2 ( x ) , · · · , T 7 ( x ) centered at 0 for the function f ( x ) = sin x using the following commands. f:=sin(x): n:=7: for i from 1 to n do; T[i]:=convert(taylor(f,x,i+1),polynom); od; We can use MAPLE to plot the graphs of each of these 7 Taylor polynomials alongside the graph of f ( x ) = sin x in the viewing rectangle - 2 π x 2 π , - 1 . 5 y 1 . 5 using the following commands. with(plots): f:=sin(x): n:=7: P[0]:=plot(f,x=-2*Pi..2*Pi,view=-1.5..1.5,color=blue): for i from 1 to n do: T[i]:=convert(taylor(f,x,i+1),polynom): P[i]:=plot(T[i],x=-2*Pi..2*Pi,color=COLOR(RGB,1,1-i/n,0)): od: display(seq(P[i],i=0..n)); If you use the above MAPLE commands to plot the graphs, you will obtain a picture similar to one which appears in section 11.11 of your textbook. Notice that the Taylor polynomials
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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 √ 4-x 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 √ 4-x 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 √ 4-x 2 in the viewing rectangle-2 ≤ 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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