What is the limit as x approaches 0 of (tan(4x))/x ?

The limit as x approaches 0 of (tan(4x))/x is 4

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limit as x approaches 0 of (tan(4x))/x

x \to 0 lim (\frac{tan ( 4 x )}{x})

4

Solution steps

x \to 0 lim (\frac{tan ( 4 x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{sec ^{2} ( 4 \cdot 0 ) \cdot 4}{1} : 4

= 4

What is the limit as x approaches 0 of (tan(4x))/x ?
The limit as x approaches 0 of (tan(4x))/x is 4