What is the limit as x approaches 0 of (sin(x))/(5x) ?

The limit as x approaches 0 of (sin(x))/(5x) is 1/5

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limit as x approaches 0 of (sin(x))/(5x)

x \to 0 lim (\frac{sin ( x )}{5 x})

\frac{1}{5}

Decimal

0.2

Solution steps

x \to 0 lim (\frac{sin ( x )}{5 x})

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{cos ( x )}{1})

Plug in the value

x = 0

= \frac{1}{5} \cdot \frac{cos ( 0 )}{1}

Simplify

\frac{1}{5} \cdot \frac{cos ( 0 )}{1} : \frac{1}{5}

= \frac{1}{5}

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What is the limit as x approaches 0 of (sin(x))/(5x) ?
The limit as x approaches 0 of (sin(x))/(5x) is 1/5