Find the third Taylor polynomial P3(x) for the function f (x) = (x 1) ln x

Find the third Taylor polynomial P3(x) for the function f (x) = (x ˆ’ 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) ˆ’ P3(0.5)| using the error formula, and compare it to the actual error.
b. Find a bound for the error |f (x) ˆ’ 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.

Transcribed Image Text:

o f(x) dx using J, P2(x) dx.