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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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 )})

Plug in the value

x = - π

= \frac{1}{sec ^{2} ( - π )}

Simplify

\frac{1}{sec ^{2} ( - π )} : 1

= 1

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