What is taylor (x^2+1)*e^{x-1},1 ?

The answer to taylor (x^2+1)*e^{x-1},1 is 2+4(x-1)+4(x-1)^2+7/3 (x-1)^3+11/12 (x-1)^4+\ldots

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taylor (x^2+1)*e^{x-1},1

taylor

(x^{2} + 1) \cdot e^{x - 1}, 1

2 + 4 (x - 1) + 4 (x - 1)^{2} + \frac{7}{3} (x - 1)^{3} + \frac{11}{12} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 2 + \frac{\frac{d}{d x} ( ( x ^{2} + 1 ) e ^{x - 1} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x ^{2} + 1 ) e ^{x - 1} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x ^{2} + 1 ) e ^{x - 1} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 2 + \frac{4}{1 !} (x - 1) + \frac{8}{2 !} (x - 1)^{2} + \frac{14}{3 !} (x - 1)^{3} + \frac{22}{4 !} (x - 1)^{4} + \dots

Refine

= 2 + 4 (x - 1) + 4 (x - 1)^{2} + \frac{7}{3} (x - 1)^{3} + \frac{11}{12} (x - 1)^{4} + \dots

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What is taylor (x^2+1)*e^{x-1},1 ?
The answer to taylor (x^2+1)*e^{x-1},1 is 2+4(x-1)+4(x-1)^2+7/3 (x-1)^3+11/12 (x-1)^4+\ldots