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

The limit as x approaches 0 of (2tan(2x))/x is 4

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

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

4

Solution steps

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

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

Plug in the value

x = 0

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

Simplify

2 \cdot \frac{sec ^{2} ( 2 \cdot 0 ) \cdot 2}{1} : 4

= 4

n = 0 \sum \infty (\frac{x}{n})^{n}

x \to π - lim (\frac{1}{sin ( x )})

y^{^{'}} = (1 - 2 t) y^{2}

\frac{d}{d x} (x^{3} cos (x^{3}))

\frac{d y}{d x} = 8 x - 4 x y

What is the limit as x approaches 0 of (2tan(2x))/x ?
The limit as x approaches 0 of (2tan(2x))/x is 4