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

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

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 x/(sin(x/4))

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

4

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

\frac{1}{cos ( \frac{0}{4} ) \frac{1}{4}} : 4

= 4

\frac{d}{d x} (e^{x} - 2 - x)

y^{^{'}} - \frac{9}{x} y = \frac{y ^{4}}{x ^{13}}, y (1) = 1

\frac{d x}{d t} - 4 x = cos (3 t), x (0) = - 1

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

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