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

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

\frac{d}{d x} (ln (π))

\int_{0}^{3} (3 t + 4) d t

\int_{- 1}^{1} ln ∣ x ∣ d x

y = \frac{13}{x ^{2} + 5 x + 6}, y = 0, x = 0, x = 1

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