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

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

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

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

- 2

Solution steps

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

Rewrite for L'Hopital

= x \to \frac{π}{2} lim (\frac{- π + 2 x}{\frac{1}{t a n ( x )}})

Apply L'Hopital's Rule

: x \to \frac{π}{2} lim (\frac{2}{- csc ^{2} ( x )})

= x \to \frac{π}{2} lim (\frac{2}{- csc ^{2} ( x )})

Plug in the value

x = \frac{π}{2}

= \frac{2}{- csc ^{2} ( \frac{π}{2} )}

Simplify

\frac{2}{- csc ^{2} ( \frac{π}{2} )} : - 2

= - 2

x \to 1 + lim (tan (x - 1))

x \to 4 lim (\frac{2 x - 4}{x - 1})

x \to - \infty lim (- (x)^{2})

x \to 3 - lim (\frac{x}{9 - x ^{2}})

x \to 1 - lim (ln (1 - x^{2}))

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