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Find the third Taylor polynomial P3(x) for the function f (x) = (x − 1) ln x about x0 = 1.
a. Use P3(0.5) to approximate f (0.5). Find an upper bound for error |f (0.5) − P3(0.5)| using the error formula, and compare it to the actual error.
b. Find a bound for the error |f (x) − P3(x)| in using P3(x) to approximate f (x) on the interval [0.5, 1.5].
c. Approximate
d. Find an upper bound for the error in (c) using
and compare the bound to the actual error. |
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