What is taylor e^{2x}-x ?

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

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taylor e^{2x}-x

taylor

e^{2 x} - x

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

10 y^{^{''}} - 10 y^{^{'}} + 125 y = 0

x \to \infty lim ((1 + \frac{1}{6 x})^{5 x})

3 t^{2}

\int_{0}^{3} 5 e^{- 3 x} d x

\int \frac{1 - x}{1 - x} d x

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