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

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

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

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

- 2

Solution steps

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

: x \to π lim (\frac{1}{- csc ^{2} ( \frac{x}{2} ) \frac{1}{2}})

= x \to π lim (\frac{1}{- csc ^{2} ( \frac{x}{2} ) \frac{1}{2}})

Plug in the value

x = π

= \frac{1}{- csc ^{2} ( \frac{π}{2} ) \frac{1}{2}}

Simplify

\frac{1}{- csc ^{2} ( \frac{π}{2} ) \frac{1}{2}} : - 2

= - 2

\frac{\partial}{\partial x} (x y + yz + zy)

n = 0 \sum \infty \frac{3 ^{n}}{5 ^{n}}

y = 6 sin (x), at x = \frac{π}{6}

\frac{\partial}{\partial y} (x y - \frac{x ^{4}}{4})

\int e^{- 2 x} sin (6 x) d x

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