What is the limit as x approaches 0 of (e^{8x}-1)/x ?

The limit as x approaches 0 of (e^{8x}-1)/x is 8

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limit as x approaches 0 of (e^{8x}-1)/x

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

8

Solution steps

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{8 e ^{8 x}}{1})

= x \to 0 lim (\frac{8 e ^{8 x}}{1})

Plug in the value

x = 0

= \frac{8 e ^{8 \cdot 0}}{1}

Simplify

= 8

(2, 1), (- 4, - 2)

\int 4 x^{2} cos (\frac{x}{5}) d x

x \to 3 - lim (\frac{2}{( x - 3 ) ^{3}})

\int \frac{x - 5}{x + 3} d x

y = (x - 2)^{2}, y = x

What is the limit as x approaches 0 of (e^{8x}-1)/x ?
The limit as x approaches 0 of (e^{8x}-1)/x is 8