What is maclaurin e^{-x},5 ?

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

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maclaurin e^{-x},5

maclaurin

e^{- x}, 5

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

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Refine

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

\int 1 + \frac{2}{y} d y

\frac{1}{2 z ^{3}}

y^{^{'}} = - \frac{2 y}{x + 1} + 2 x

x \to 4 lim (x^{2} - 1)

\int x ln^{5} (x) d x

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