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

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

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

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

a

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= a

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