What is taylor e^{(x+1)} ?

The answer to taylor e^{(x+1)} is e+ex+e/2 x^2+e/6 x^3+e/(24)x^4+\ldots

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taylor e^{(x+1)}

taylor

e^{(x + 1)}

e + e x + \frac{e}{2} x^{2} + \frac{e}{6} x^{3} + \frac{e}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= e + \frac{\frac{d}{d x} ( e ^{x + 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x + 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{x + 1} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= e + \frac{e}{1 !} x + \frac{e}{2 !} x^{2} + \frac{e}{3 !} x^{3} + \frac{e}{4 !} x^{4} + \dots

Refine

= e + e x + \frac{e}{2} x^{2} + \frac{e}{6} x^{3} + \frac{e}{24} x^{4} + \dots

What is taylor e^{(x+1)} ?
The answer to taylor e^{(x+1)} is e+ex+e/2 x^2+e/6 x^3+e/(24)x^4+\ldots