What is the limit as x approaches 0 of (sin(18x))/x ?

The limit as x approaches 0 of (sin(18x))/x is 18

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limit as x approaches 0 of (sin(18x))/x

x \to 0 lim (\frac{sin ( 18 x )}{x})

18

Solution steps

x \to 0 lim (\frac{sin ( 18 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 18 x ) \cdot 18}{1})

= x \to 0 lim (\frac{cos ( 18 x ) \cdot 18}{1})

Plug in the value

x = 0

= \frac{cos ( 18 \cdot 0 ) \cdot 18}{1}

Simplify

\frac{cos ( 18 \cdot 0 ) \cdot 18}{1} : 18

= 18

x \to 3 lim (4 x + 5)

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x \to \frac{1}{3} lim (6 x - 1)

x \to 0 lim (x (ln (x) - 1))

x \to 0 lim ((1 + \frac{2}{x})^{3 x})

What is the limit as x approaches 0 of (sin(18x))/x ?
The limit as x approaches 0 of (sin(18x))/x is 18