What is the limit as x approaches 0 of (e^x-1)/(11x) ?

The limit as x approaches 0 of (e^x-1)/(11x) is 1/11

Popular >

limit as x approaches 0 of (e^x-1)/(11x)

x \to 0 lim (\frac{e ^{x} - 1}{11 x})

\frac{1}{11}

Decimal Notation

0.09090 \dots

Solution steps

x \to 0 lim (\frac{e ^{x} - 1}{11 x})

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

= \frac{1}{11} \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}{11} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Plug in the value

x = 0

= \frac{1}{11} \cdot \frac{e ^{0}}{1}

Simplify

\frac{1}{11} \cdot \frac{e ^{0}}{1} : \frac{1}{11}

= \frac{1}{11}

x \to - 3 lim (\frac{9 - x ^{2}}{x + 3})

\frac{\partial}{\partial x} (ln (\frac{x}{1 - x}))

t sin (3 t)

\int (x^{10} - 5 x^{2})^{3} (x^{9} - x) d x

What is the limit as x approaches 0 of (e^x-1)/(11x) ?
The limit as x approaches 0 of (e^x-1)/(11x) is 1/11