What is maclaurin (4x^2)e^{-10x} ?

The answer to maclaurin (4x^2)e^{-10x} is 4x^2-40x^3+200x^4-2000/3 x^5+5000/3 x^6+\ldots

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maclaurin (4x^2)e^{-10x}

maclaurin

(4 x^{2}) e^{- 10 x}

4 x^{2} - 40 x^{3} + 200 x^{4} - \frac{2000}{3} x^{5} + \frac{5000}{3} x^{6} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( 4 x ^{2} e ^{- 10 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 x ^{2} e ^{- 10 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 x ^{2} e ^{- 10 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{8}{2 !} x^{2} + \frac{- 240}{3 !} x^{3} + \frac{4800}{4 !} x^{4} + \frac{- 80000}{5 !} x^{5} + \frac{1200000}{6 !} x^{6} + \dots

Refine

= 4 x^{2} - 40 x^{3} + 200 x^{4} - \frac{2000}{3} x^{5} + \frac{5000}{3} x^{6} + \dots

x \to \frac{π}{2} lim (\frac{tan ( x ) - sec ( x )}{cos ( x )})

x \to 0 lim (7 csc (x) - \frac{7}{x})

y^{^{''}} - (\frac{4}{x}) y^{^{'}} - (\frac{8}{x ^{2}}) y = 0

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

y = \frac{6}{x ^{4}} - \frac{4}{x ^{2}} - \frac{3}{x}

What is maclaurin (4x^2)e^{-10x} ?
The answer to maclaurin (4x^2)e^{-10x} is 4x^2-40x^3+200x^4-2000/3 x^5+5000/3 x^6+\ldots