Apply [2.17] to construct a quadratic
polynomial approximation for the function
about the point
= 0.
Solution
Formula [2.17] provides a quadratic
polynomial approximation p2(x) for the function f(x).
[2.17]
We have
[s1]
so
[s2]
[s3]
Valuing [s1], [s2], and [s3] at
= 0, we obtain values 0, 1, and 2 respectively. Substituting these values
into [2.17], we obtain the quadratic approximation
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about the point
= 0.
