What is the limit as x approaches 0 of (e^x-1)/(19x) ?

The limit as x approaches 0 of (e^x-1)/(19x) is 1/19

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limit as x approaches 0 of (e^x-1)/(19x)

x \to 0 lim (\frac{e ^{x} - 1}{19 x})

\frac{1}{19}

Decimal

0.05263 \dots

Solution steps

x \to 0 lim (\frac{e ^{x} - 1}{19 x})

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

= \frac{1}{19} \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}{19} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Plug in the value

x = 0

= \frac{1}{19} \cdot \frac{e ^{0}}{1}

Simplify

\frac{1}{19} \cdot \frac{e ^{0}}{1} : \frac{1}{19}

= \frac{1}{19}

x \to - 2 lim (3 x)

\frac{d y}{d x} = 7 x e^{y}, y (0) = 0

\frac{d}{d x} (- 3 cos^{2} (x) sin (x))

\int \frac{1}{x ( x ^{2} - 9 ) ^{\frac{3}{2}}} d x

\frac{d y}{d x} = 2 (y^{2} + 1)

What is the limit as x approaches 0 of (e^x-1)/(19x) ?
The limit as x approaches 0 of (e^x-1)/(19x) is 1/19