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

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

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limit as x approaches pi of (2x-2pi)cot(x)

x \to π lim ((2 x - 2 π) cot (x))

2

Solution steps

x \to π lim ((2 x - 2 π) cot (x))

Rewrite for L'Hopital

= x \to π lim (\frac{2 x - 2 π}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

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

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

Plug in the value

x = π

= \frac{2}{sec ^{2} ( π )}

Simplify

\frac{2}{sec ^{2} ( π )} : 2

= 2

\frac{d}{d x} (cos (x^{2} - 1))

\frac{\partial}{\partial x} (\frac{6 x}{x ^{2} + y ^{2}})

y^{^{'}} = 2 x + y, y (0) = 7

sin (x) (cos (x) - 1) π

\frac{\partial}{\partial x} (x^{2} + 4 y^{2})

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