What is maclaurin e^{-5x} ?

The answer to maclaurin e^{-5x} is 1-5x+25/2 x^2-125/6 x^3+625/24 x^4+\ldots

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maclaurin e^{-5x}

maclaurin

e^{- 5 x}

1 - 5 x + \frac{25}{2} x^{2} - \frac{125}{6} x^{3} + \frac{625}{24} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 5 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 5 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 5 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 5}{1 !} x + \frac{25}{2 !} x^{2} + \frac{- 125}{3 !} x^{3} + \frac{625}{4 !} x^{4} + \dots

Refine

= 1 - 5 x + \frac{25}{2} x^{2} - \frac{125}{6} x^{3} + \frac{625}{24} x^{4} + \dots

3 y^{^{'}} - 6 y = 12

\int cos^{4} (3 x) sin (3 x) d x

t \frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} = t^{2}

y = - \frac{3}{2} x^{2} + 9 x + 9, (- 1, - \frac{3}{2})

\int 7 - x^{2} d x

What is maclaurin e^{-5x} ?
The answer to maclaurin e^{-5x} is 1-5x+25/2 x^2-125/6 x^3+625/24 x^4+\ldots