What is maclaurin e^{-2x} ?

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

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maclaurin e^{-2x}

maclaurin

e^{- 2 x}

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

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Refine

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

\int \frac{x ^{3}}{7 x ^{2} + 1} d x

\int \frac{x ^{2} + 2}{x ^{2}} d x

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{2}} d x

\int_{1}^{3} \frac{3}{x ^{2}} d x

\int \frac{x ^{4}}{( 3 - x ^{5} ) ^{2}} d x

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