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

The limit as x approaches 0 of (2tan(x/2))/x is 1

Popular >

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 1

\int tan^{5} (6 x) sec^{2} (6 x) d x

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})

f (x) = ln (5) x^{4}

\frac{d}{d x} (\frac{2}{( x + 2 ) ^{3}})

\frac{\partial}{\partial x} (7 - x^{2} + x y - 2 y^{2})

What is the limit as x approaches 0 of (2tan(x/2))/x ?
The limit as x approaches 0 of (2tan(x/2))/x is 1