What is the limit as x approaches 0 of (tan^2(3x))/x ?

The limit as x approaches 0 of (tan^2(3x))/x is 0

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limit as x approaches 0 of (tan^2(3x))/x

x \to 0 lim (\frac{tan ^{2} ( 3 x )}{x})

0

Solution steps

x \to 0 lim (\frac{tan ^{2} ( 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{6 sec ^{2} ( 3 x ) tan ( 3 x )}{1})

= x \to 0 lim (\frac{6 sec ^{2} ( 3 x ) tan ( 3 x )}{1})

Plug in the value

x = 0

= \frac{6 sec ^{2} ( 3 \cdot 0 ) tan ( 3 \cdot 0 )}{1}

Simplify

\frac{6 sec ^{2} ( 3 \cdot 0 ) tan ( 3 \cdot 0 )}{1} : 0

= 0

\frac{d}{d x} (f (x) (x)^{2})

\frac{d y}{d x} = \frac{y ^{2}}{x ^{2}} + \frac{y}{x} + 1

\frac{d}{d x} (\frac{x ^{2} - 10 x + 2}{x ( x ^{2} - 1 )})

\frac{d}{d x} (\frac{x ^{5}}{3 - x ^{4}})

\frac{d}{d x} (\frac{sin ^{2} ( x )}{4})

What is the limit as x approaches 0 of (tan^2(3x))/x ?
The limit as x approaches 0 of (tan^2(3x))/x is 0