What is taylor 2e^x ?

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

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taylor 2e^x

taylor

2 e^{x}

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

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