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Find the second Taylor polynomial P2(x) for the function f (x) = ex cos x about x0 = 0.
a. Use P2 (0.5) to approximate f (0.5). Find an upper bound for error |f (0.5) − P2(0.5)| using the error formula, and compare it to the actual error.
b. Find a bound for the error |f(x)−P2(x)| in using P2(x) to approximate f (x) on the interval [0, 1].
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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