What is the limit as x approaches 0 of (e^x-1)/(20x) ?

The limit as x approaches 0 of (e^x-1)/(20x) is 1/20

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limit as x approaches 0 of (e^x-1)/(20x)

x \to 0 lim (\frac{e ^{x} - 1}{20 x})

\frac{1}{20}

Decimal Notation

0.05

Solution steps

x \to 0 lim (\frac{e ^{x} - 1}{20 x})

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

= \frac{1}{20} \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}{20} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Plug in the value

x = 0

= \frac{1}{20} \cdot \frac{e ^{0}}{1}

Simplify

\frac{1}{20} \cdot \frac{e ^{0}}{1} : \frac{1}{20}

= \frac{1}{20}

\frac{\partial}{\partial x} (\frac{7 x z}{x + y})

\int (4 t - 2) (e^{t^{2} - t}) d t

\int_{- 3}^{0} (4 + 9 - x^{2}) d x

\frac{d}{d x} (64 (x + 2)^{3})

x \to 4 lim (\frac{4 - x}{∣ 4 - x ∣})

What is the limit as x approaches 0 of (e^x-1)/(20x) ?
The limit as x approaches 0 of (e^x-1)/(20x) is 1/20