What is the limit as x approaches 0 of (e^{x/2}-1)/x ?

The limit as x approaches 0 of (e^{x/2}-1)/x is 1/2

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limit as x approaches 0 of (e^{x/2}-1)/x

x \to 0 lim (\frac{e ^{\frac{x}{2}} - 1}{x})

\frac{1}{2}

Decimal

0.5

Solution steps

x \to 0 lim (\frac{e ^{\frac{x}{2}} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{\frac{1}{2} e ^{\frac{x}{2}}}{1})

= x \to 0 lim (\frac{\frac{1}{2} e ^{\frac{x}{2}}}{1})

Plug in the value

x = 0

= \frac{\frac{1}{2} e ^{\frac{0}{2}}}{1}

Simplify

\frac{\frac{1}{2} e ^{\frac{0}{2}}}{1} : \frac{1}{2}

= \frac{1}{2}

x \to 0 lim (\frac{a ^{x}}{x})

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

x \to 0 lim (\frac{cos ( x ) + x}{x})

x \to 0 lim (lo g_{e} (∣ x ∣))

x \to \infty lim (ln (e x))

What is the limit as x approaches 0 of (e^{x/2}-1)/x ?
The limit as x approaches 0 of (e^{x/2}-1)/x is 1/2