What is the limit as x approaches 0 of (tan(3x))/x ?

The limit as x approaches 0 of (tan(3x))/x is 3

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limit as x approaches 0 of (tan(3x))/x

x \to 0 lim (\frac{tan ( 3 x )}{x})

3

Solution steps

x \to 0 lim (\frac{tan ( 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 3 x ) \cdot 3}{1})

= x \to 0 lim (\frac{sec ^{2} ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

\frac{sec ^{2} ( 3 \cdot 0 ) \cdot 3}{1} : 3

= 3

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What is the limit as x approaches 0 of (tan(3x))/x ?
The limit as x approaches 0 of (tan(3x))/x is 3