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

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

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Apply L'Hopital's Rule

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= \frac{1}{2}

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