What is the limit as x approaches 0 of (sin(10x))/x ?

The limit as x approaches 0 of (sin(10x))/x is 10

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(10x))/x

x \to 0 lim (\frac{sin ( 10 x )}{x})

10

Solution steps

x \to 0 lim (\frac{sin ( 10 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 10 x ) \cdot 10}{1})

= x \to 0 lim (\frac{cos ( 10 x ) \cdot 10}{1})

Plug in the value

x = 0

= \frac{cos ( 10 \cdot 0 ) \cdot 10}{1}

Simplify

\frac{cos ( 10 \cdot 0 ) \cdot 10}{1} : 10

= 10

\int_{0}^{2} \frac{4 x + 3}{x ^{4}} d x

\int (5 x^{3} - 7 x^{2} + 2 x + 1) d x

\frac{d}{d x} (30 + \frac{1}{x + 1} - 3 x^{2})

\frac{d}{d x} (\frac{1}{5 x ^{2} + 2 x})

\frac{5 s + 3}{( s - 1 ) ( s ^{2} + 2 s + 5 )}

What is the limit as x approaches 0 of (sin(10x))/x ?
The limit as x approaches 0 of (sin(10x))/x is 10