What is the limit as x approaches 0 of xcsc(x) ?

The limit as x approaches 0 of xcsc(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 0 of xcsc(x)

x \to 0 lim (x csc (x))

1

Solution steps

x \to 0 lim (x csc (x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x}{\frac{1}{c s c ( x )}})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= \frac{1}{cos ( 0 )}

Simplify

\frac{1}{cos ( 0 )} : 1

= 1

What is the limit as x approaches 0 of xcsc(x) ?
The limit as x approaches 0 of xcsc(x) is 1