What is the limit as x approaches 0 of (e^x-1)/(17x) ?

The limit as x approaches 0 of (e^x-1)/(17x) is 1/17

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limit as x approaches 0 of (e^x-1)/(17x)

x \to 0 lim (\frac{e ^{x} - 1}{17 x})

\frac{1}{17}

Decimal Notation

0.05882 \dots

Solution steps

x \to 0 lim (\frac{e ^{x} - 1}{17 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{17} \cdot x \to 0 lim (\frac{e ^{x} - 1}{x})

Apply L'Hopital's Rule

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

= \frac{1}{17} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Plug in the value

x = 0

= \frac{1}{17} \cdot \frac{e ^{0}}{1}

Simplify

\frac{1}{17} \cdot \frac{e ^{0}}{1} : \frac{1}{17}

= \frac{1}{17}

f (x) = 3^{x} - 5 e^{x}

\frac{d}{d x} (x^{3} - 7)

\frac{1}{1 + x}

\int 9 x e^{(- 3 x)} d x

f (x) = 3 - x^{2}, at x = 4

What is the limit as x approaches 0 of (e^x-1)/(17x) ?
The limit as x approaches 0 of (e^x-1)/(17x) is 1/17