What is the limit as x approaches 0 of (tan(6x))/x ?

The limit as x approaches 0 of (tan(6x))/x is 6

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limit as x approaches 0 of (tan(6x))/x

x \to 0 lim (\frac{tan ( 6 x )}{x})

6

Solution steps

x \to 0 lim (\frac{tan ( 6 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 6 x ) \cdot 6}{1})

= x \to 0 lim (\frac{sec ^{2} ( 6 x ) \cdot 6}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 6 \cdot 0 ) \cdot 6}{1}

Simplify

\frac{sec ^{2} ( 6 \cdot 0 ) \cdot 6}{1} : 6

= 6

f (x) = 3 e^{x} x

\frac{\partial}{\partial x} (\frac{2 s - 3 y}{3 s + 5 y})

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

x \to \frac{π}{3} lim (tan (x))

\frac{d}{d x} (a x e^{x} + a e^{x})

What is the limit as x approaches 0 of (tan(6x))/x ?
The limit as x approaches 0 of (tan(6x))/x is 6