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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 0

x \to 0 lim (1 + \frac{tan ( x )}{x})

x \to - 1 lim ([x] + [- x])

x \to 0 lim (\frac{x ^{2} - 5 x}{x ^{2} + 8 x})

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

x \to - \infty lim (\frac{x}{0})

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