Find the third Taylor polynomial P(x) for the function f(x) = (x ? 1) In x about X0 = 1.
a. Use P1(O.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)I in using P3(x) to approximate f(x) on the interval [0.5, 1.5].
Taylor Polynomials and Error Formulas are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.