What is the limit as x approaches 0 of (e^{4x}-1)/x ?

The limit as x approaches 0 of (e^{4x}-1)/x is 4

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limit as x approaches 0 of (e^{4x}-1)/x

x \to 0 lim (\frac{e ^{4 x} - 1}{x})

4

Solution steps

x \to 0 lim (\frac{e ^{4 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{4 e ^{4 x}}{1})

= x \to 0 lim (\frac{4 e ^{4 x}}{1})

Plug in the value

x = 0

= \frac{4 e ^{4 \cdot 0}}{1}

Simplify

= 4

\frac{2}{t - 3}

y y^{^{'}} - 4 e^{x} = 0, y (0) = 3

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

\frac{\partial}{\partial x} (y^{\frac{y}{x}} sin (\frac{y}{x}))

(- 2.7) (4.3)

What is the limit as x approaches 0 of (e^{4x}-1)/x ?
The limit as x approaches 0 of (e^{4x}-1)/x is 4