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

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

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

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

0

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 0

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