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

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

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

x \to π lim ((π - x) cot (x))

- 1

Solution steps

x \to π lim ((π - x) 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

(e^{- 1}) (sin (2 t))

e^{8 x} cos (11 x)

\int X^{- 1} d X

3 x y

\int \frac{1}{1 + x + 1} d x

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