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

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

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limit as x approaches pi/2 of (tan(2x))/(x-pi/2)

x \to \frac{π}{2} lim (\frac{tan ( 2 x )}{x - \frac{π}{2}})

2

Solution steps

x \to \frac{π}{2} lim (\frac{tan ( 2 x )}{x - \frac{π}{2}})

Apply L'Hopital's Rule

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

Plug in the value

x = \frac{π}{2}

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

Simplify

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

= 2

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