What is taylor e^x2 ?

The answer to taylor e^x2 is 2+2x+x^2+1/3 x^3+1/12 x^4+\ldots

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taylor e^x2

taylor

e^{x} 2

2 + 2 x + x^{2} + \frac{1}{3} x^{3} + \frac{1}{12} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 2 + 2 x + x^{2} + \frac{1}{3} x^{3} + \frac{1}{12} x^{4} + \dots

\int cos (x) e^{x} d x

\int \frac{4 x ^{2} - 7 x - 19}{x ^{2} - 2 x - 3} d x

- 3 a e^{- 3 x} + b e^{x} + c (e^{x} + e^{x} x)

\frac{1}{2} (e^{(1 - x)})

y = - \frac{12}{7} x = + b

What is taylor e^x2 ?
The answer to taylor e^x2 is 2+2x+x^2+1/3 x^3+1/12 x^4+\ldots