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

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

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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})

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{2}

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