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\noindent {\bf Problem statement} Suppose $
f(x)=(1-x)^{-1/2}={1\over{\sqrt{1-x}}}.$ 

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\noindent a) Find the fourth Taylor polynomial, $T_4(x)$, centered at
$a=0$ for $f$.

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\noindent b) Sketch the graphs of $y=f(x)$ and $y=T_4(x)$ in the
window $[-1,1]\times [0,3]$.

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\noindent c) Sketch the graph of $f(x)-T_4(x)$ in the window $[-.5,
5]\times [-.01,.01]$.

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\font\ssb=cmssbx10.tfm

\noindent d) Use Taylor's inequality (the {\ssb Error Bound}) to find
an overestimate for $|f(x)-T_4(x)|$ on the interval $[-.5, .5]$. Your
answer should be an explicit number valid for every $x$ on this
interval.










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