What is taylor 1+e^{2x} ?

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

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taylor 1+e^{2x}

taylor

1 + e^{2 x}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{8}{3 !} x^{3} + \frac{16}{4 !} x^{4} + \dots

Refine

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

\int sec^{2} (x) - 5 d x

\frac{d y}{d t} = 2 \cdot y

x^{2} - 5

x \to \infty lim (- 3 e^{x})

\frac{d}{d x} (- \frac{y}{y ^{2} + x ^{2}})

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