What is maclaurin (x^2)/(e^x) ?

The answer to maclaurin (x^2)/(e^x) is x^2-x^3+1/2 x^4-1/6 x^5+1/24 x^6+\ldots

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maclaurin (x^2)/(e^x)

maclaurin

\frac{x ^{2}}{e ^{x}}

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

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \frac{- 20}{5 !} x^{5} + \frac{30}{6 !} x^{6} + \dots

Refine

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

\int_{0}^{1} e^{- 4 x} d x

\frac{d}{d x} (C e^{- 2 x})

\int 3^{s i n (x)} cos (x) d x

P^{^{'}} = k P

9 t

What is maclaurin (x^2)/(e^x) ?
The answer to maclaurin (x^2)/(e^x) is x^2-x^3+1/2 x^4-1/6 x^5+1/24 x^6+\ldots