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

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

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

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

2

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 2

\int \frac{3}{1 + 3 x} d x

\frac{\partial}{\partial x} (6 x^{2} y)

d y = \frac{x + 6}{x + 1} d x

y = 4 sin (5 x - 2)

(t^{2} + 1) \frac{d y}{d t} = y t - y

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