What is the limit as x approaches 0 of (e^{5x}-1)/x ?

The limit as x approaches 0 of (e^{5x}-1)/x is 5

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limit as x approaches 0 of (e^{5x}-1)/x

x \to 0 lim (\frac{e ^{5 x} - 1}{x})

5

Solution steps

x \to 0 lim (\frac{e ^{5 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{5 e ^{5 x}}{1})

= x \to 0 lim (\frac{5 e ^{5 x}}{1})

Plug in the value

x = 0

= \frac{5 e ^{5 \cdot 0}}{1}

Simplify

= 5

\int cos (5 x) sin (x) sin (8 x) d x

\frac{d y}{d x} = \frac{x cos ( x ^{2} )}{4 y}

\frac{d}{d x} (cos^{2} (x) + cos (x^{2}))

y^{^{'}} = - \frac{x}{4 y}

y = (sin (3 x)) ln (x)

What is the limit as x approaches 0 of (e^{5x}-1)/x ?
The limit as x approaches 0 of (e^{5x}-1)/x is 5