What is the limit as x approaches 0 of 3xcsc(x) ?

The limit as x approaches 0 of 3xcsc(x) is 3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0 of 3xcsc(x)

x \to 0 lim (3 x csc (x))

3

Solution steps

x \to 0 lim (3 x csc (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 0 lim (x csc (x))

Rewrite for L'Hopital

= 3 \cdot 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 )})

= 3 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 3 \cdot \frac{1}{cos ( 0 )}

Simplify

3 \cdot \frac{1}{cos ( 0 )} : 3

= 3

x \to 0 + lim (x^{3} sin (\frac{1}{x}))

x \to 2 lim (\frac{x}{4 - x ^{2}})

x \to 2 lim (9 x^{2} - 2 x)

x \to 0 lim (\frac{x}{1 + ∣ x ∣})

x \to 0 lim (\frac{ln ( x )}{1 + 2 ln ( sin ( x ) )})

What is the limit as x approaches 0 of 3xcsc(x) ?
The limit as x approaches 0 of 3xcsc(x) is 3