What is the limit as x approaches 0 of x(csc(4x)) ?

The limit as x approaches 0 of x(csc(4x)) is 1/4

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 x(csc(4x))

x \to 0 lim (x (csc (4 x)))

\frac{1}{4}

Decimal

0.25

Solution steps

x \to 0 lim (x csc (4 x))

Express with sin, cos

= x \to 0 lim (\frac{x}{sin ( 4 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{cos ( 4 x ) \cdot 4})

Plug in the value

x = 0

= \frac{1}{cos ( 4 \cdot 0 ) \cdot 4}

cos (4 \cdot 0) \cdot 4 = 4

= \frac{1}{4}

x \to \infty lim (\frac{cosh ( x )}{e ^{x}})

x \to - 1 lim (3 x^{3} - 4 x^{2} - 3)

x \to 0 lim (e^{\frac{2}{x}})

x \to 2 lim (x^{3} + 2 x - 8)

x \to 0 lim (\frac{x - 3}{x ^{2} - 9})

What is the limit as x approaches 0 of x(csc(4x)) ?
The limit as x approaches 0 of x(csc(4x)) is 1/4