What is the limit as x approaches 0 of (e^{9x}-1)/x ?

The limit as x approaches 0 of (e^{9x}-1)/x is 9

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limit as x approaches 0 of (e^{9x}-1)/x

x \to 0 lim (\frac{e ^{9 x} - 1}{x})

9

Solution steps

x \to 0 lim (\frac{e ^{9 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{9 e ^{9 x}}{1})

= x \to 0 lim (\frac{9 e ^{9 x}}{1})

Plug in the value

x = 0

= \frac{9 e ^{9 \cdot 0}}{1}

Simplify

= 9

\frac{d y}{d x} + \frac{3}{x} y = 2 x + 5

\frac{x}{( x + 2 ) ( x ^{2} + 4 )}

\int \frac{ln ( x )}{x ^{5}} d x

\int_{0}^{4} x^{2} (4 - x)^{3} d x

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

What is the limit as x approaches 0 of (e^{9x}-1)/x ?
The limit as x approaches 0 of (e^{9x}-1)/x is 9