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

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

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

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

2

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 2

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\int csc^{2} (1) d x

f (x) = \frac{x ^{3} - 1}{2 x + 3}

(1 + 3 x^{2}) (x - x^{2})

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