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

The limit as x approaches pi of (x-pi)cot(x) is 1

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

x \to π lim ((x - π) cot (x))

1

Solution steps

x \to π lim ((x - π) cot (x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = π

= \frac{1}{sec ^{2} ( π )}

Simplify

\frac{1}{sec ^{2} ( π )} : 1

= 1

\int_{0}^{1} 2 x - 3 d x

\int sin^{2 x} (d) x d x

\int_{0}^{1} sin (π x) d x

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

y^{^{'}} = 3 x^{2} y + 2 x y

What is the limit as x approaches pi of (x-pi)cot(x) ?
The limit as x approaches pi of (x-pi)cot(x) is 1