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

The answer to maclaurin e^{(-x)/2} is 1-1/2 x+1/8 x^2-1/48 x^3+1/384 x^4+\ldots

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maclaurin e^{(-x)/2}

maclaurin

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

1 - \frac{1}{2} x + \frac{1}{8} x^{2} - \frac{1}{48} x^{3} + \frac{1}{384} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{2}}{1 !} x + \frac{\frac{1}{4}}{2 !} x^{2} + \frac{- \frac{1}{8}}{3 !} x^{3} + \frac{\frac{1}{16}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{1}{2} x + \frac{1}{8} x^{2} - \frac{1}{48} x^{3} + \frac{1}{384} x^{4} + \dots

f (t) = 2 - \frac{4}{t}

e^{3 x}

\frac{d}{d x} (arccos (arcsin (x)))

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 x)

y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

What is maclaurin e^{(-x)/2} ?
The answer to maclaurin e^{(-x)/2} is 1-1/2 x+1/8 x^2-1/48 x^3+1/384 x^4+\ldots