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

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

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

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

2

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 2

\frac{d y}{d x} = \frac{x + y ^{2}}{2 y}, y (0) = 1

\int \frac{x ^{5}}{x ^{6} - 7} d x

f (x) = arccos (4 x^{2})

θ \to 0 lim (\frac{1}{11})

sin^{2} (x)

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