What is the limit as x approaches 0 of (tan(12x))/x ?

The limit as x approaches 0 of (tan(12x))/x is 12

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limit as x approaches 0 of (tan(12x))/x

x \to 0 lim (\frac{tan ( 12 x )}{x})

12

Solution steps

x \to 0 lim (\frac{tan ( 12 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 12 x ) \cdot 12}{1})

= x \to 0 lim (\frac{sec ^{2} ( 12 x ) \cdot 12}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 12 \cdot 0 ) \cdot 12}{1}

Simplify

\frac{sec ^{2} ( 12 \cdot 0 ) \cdot 12}{1} : 12

= 12

x \to \infty lim (3 x + 7)

- \frac{6 x}{x ^{2} + 1}

w \to - 2 lim (\frac{w ^{2} + 5 w + 6}{w ^{3} + 8})

\frac{( e ^{2 x} )}{x ^{2} + 1}

\frac{d}{d x} (x^{2} - x + 3)

What is the limit as x approaches 0 of (tan(12x))/x ?
The limit as x approaches 0 of (tan(12x))/x is 12