What is taylor e^{x+2} ?

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

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taylor e^{x+2}

taylor

e^{x + 2}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

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