What is the limit as x approaches 0 of (6sin(x))/x ?

The limit as x approaches 0 of (6sin(x))/x is 6

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 (6sin(x))/x

x \to 0 lim (\frac{6 sin ( x )}{x})

6

Solution steps

x \to 0 lim (\frac{6 sin ( x )}{x})

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

= 6 \cdot x \to 0 lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

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

= 6 \cdot x \to 0 lim (\frac{cos ( x )}{1})

Plug in the value

x = 0

= 6 \cdot \frac{cos ( 0 )}{1}

Simplify

6 \cdot \frac{cos ( 0 )}{1} : 6

= 6

\int_{0}^{1} \frac{4}{x ^{2} + 1} d x

\int \frac{( x + 1 )}{x ^{3} + x} d x

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

\frac{d}{d x} (2 (x + 4)^{\frac{3}{2}})

What is the limit as x approaches 0 of (6sin(x))/x ?
The limit as x approaches 0 of (6sin(x))/x is 6