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

x \to - 1 lim (\frac{x}{x ^{2} - 1} - 10)

x \to 0 lim (\frac{tan ( 4 ( - 0.1 ) )}{( - 0.1 )})

x \to - 2 lim (- 6 x - 7)

x \to \infty lim (\frac{2 + x ^{3}}{100 + 8 x ^{2}})

x \to - 5 lim (\frac{( x ^{2} - 25 )}{( x - 5 )})

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