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})

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

\frac{\partial}{\partial y} (sin (x^{2} - y))

\int (tan^{3} (x)) d x

y = x^{2}, y = x + 2, 0

y = \frac{x}{x ^{2} - 4 x + 5}, y = \frac{3}{x ^{2} - 4 x + 5}, x = 0

y = \frac{x ^{3} + 1}{6 x}, x = 1

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