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

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

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

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

a

Solution steps

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

Apply L'Hopital's Rule

= x \to 0 lim (\frac{sec ^{2} ( a x ) a}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( a \cdot 0 ) a}{1}

Simplify

\frac{sec ^{2} ( a \cdot 0 ) a}{1} : a

= a

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