What is the limit as x approaches 0 of (e^x-1)/(7x) ?

The limit as x approaches 0 of (e^x-1)/(7x) is 1/7

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limit as x approaches 0 of (e^x-1)/(7x)

x \to 0 lim (\frac{e ^{x} - 1}{7 x})

\frac{1}{7}

Decimal Notation

0.14285 \dots

Solution steps

x \to 0 lim (\frac{e ^{x} - 1}{7 x})

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

= \frac{1}{7} \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}{7} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Plug in the value

x = 0

= \frac{1}{7} \cdot \frac{e ^{0}}{1}

Simplify

\frac{1}{7} \cdot \frac{e ^{0}}{1} : \frac{1}{7}

= \frac{1}{7}

\frac{\partial}{\partial x} (- 5 e^{- 5 y} sin (5 x))

x \to 2 lim (2 - x)

\frac{d}{d t} (\frac{2}{2 - cos ( π t )})

\frac{d}{d x} (2 e^{c o s (\frac{x}{2})})

\frac{( x ^{2} - 3 x )}{x + 1}

What is the limit as x approaches 0 of (e^x-1)/(7x) ?
The limit as x approaches 0 of (e^x-1)/(7x) is 1/7