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Taylor and Maclaurin Polynomials — Approximate Functions with Polynomials

P_n(x) = f(a) + f'(a)(x−a) + f''(a)/2!(x−a)² + … + f^(n)(a)/n!(x−a)^n. Maclaurin: a=0.

CalculusCommon Core LIM-8.ASERVerified correct ✓

Worked examples

Find the degree-4 Maclaurin polynomial P_4(x) for f(x) = cos(x). Then evaluate P_4(-1.0). Round to 4 decimal places.
Answer: 0.5417
Find the degree-4 Maclaurin polynomial P_4(x) for f(x) = e^x. Then evaluate P_4(0.5). Round to 4 decimal places.
Answer: 1.6484

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