What is the limit as x approaches 0-of (sin(3x))/x ?

The limit as x approaches 0-of (sin(3x))/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 (sin(3x))/x

x \to 0 - lim (\frac{sin ( 3 x )}{x})

3

Solution steps

x \to 0 - lim (\frac{sin ( 3 x )}{x})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 3

x \to 7 lim (\frac{8}{x ^{2} - 49})

x \to \infty lim (2 x + \frac{5}{x})

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

x \to 0 lim (x^{2} cot (4) x^{2})

x \to \infty lim ((1 + \frac{10}{x})^{\frac{x}{9}})

What is the limit as x approaches 0-of (sin(3x))/x ?
The limit as x approaches 0-of (sin(3x))/x is 3