What is the limit as x approaches 0 of (3sin(2x))/x ?

The limit as x approaches 0 of (3sin(2x))/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 (3sin(2x))/x

x \to 0 lim (\frac{3 sin ( 2 x )}{x})

6

Solution steps

x \to 0 lim (\frac{3 sin ( 2 x )}{x})

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

= 3 \cdot x \to 0 lim (\frac{sin ( 2 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

= 3 \cdot x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

Plug in the value

x = 0

= 3 \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

3 \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : 6

= 6

x y^{^{'}} - 4 y = 6 x^{4} e^{x}

f (x) = \frac{- 4 x}{x ^{2} + 1}, at x = - 1

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

\frac{d}{d x} (x^{4} + y^{4} + z^{4})

\frac{d}{d x} (sin (7 x^{2}))

What is the limit as x approaches 0 of (3sin(2x))/x ?
The limit as x approaches 0 of (3sin(2x))/x is 6