What is maclaurin x-e^{3x} ?

The answer to maclaurin x-e^{3x} is -1-2x-9/2 x^2-9/2 x^3-27/8 x^4+\ldots

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maclaurin x-e^{3x}

maclaurin

x - e^{3 x}

- 1 - 2 x - \frac{9}{2} x^{2} - \frac{9}{2} x^{3} - \frac{27}{8} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= - 1 + \frac{- 2}{1 !} x + \frac{- 9}{2 !} x^{2} + \frac{- 27}{3 !} x^{3} + \frac{- 81}{4 !} x^{4} + \dots

Refine

= - 1 - 2 x - \frac{9}{2} x^{2} - \frac{9}{2} x^{3} - \frac{27}{8} x^{4} + \dots

\int \frac{3}{8 + 6 x} d x

y = \frac{1}{x}, y = \frac{1}{4} x

x \to 1 lim (\frac{x + 2}{x ^{3} + 8})

\int \frac{2}{x ln ^{3} ( x )} d x

What is maclaurin x-e^{3x} ?
The answer to maclaurin x-e^{3x} is -1-2x-9/2 x^2-9/2 x^3-27/8 x^4+\ldots