What is the limit as x approaches 0 of (sin(x))/(9x) ?

The limit as x approaches 0 of (sin(x))/(9x) is 1/9

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(x))/(9x)

x \to 0 lim (\frac{sin ( x )}{9 x})

\frac{1}{9}

Decimal Notation

0.11111 \dots

Solution steps

x \to 0 lim (\frac{sin ( x )}{9 x})

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

= \frac{1}{9} \cdot x \to 0 lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

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

= \frac{1}{9} \cdot x \to 0 lim (\frac{cos ( x )}{1})

Plug in the value

x = 0

= \frac{1}{9} \cdot \frac{cos ( 0 )}{1}

Simplify

\frac{1}{9} \cdot \frac{cos ( 0 )}{1} : \frac{1}{9}

= \frac{1}{9}

6 x^{2} y^{^{''}} + 13 x y^{^{'}} + y = 70 x + 2

\int_{- 2}^{1} 2 x + 4 d x

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

x \frac{d y}{d x} + 2 y = 4 e^{x}

\int 3 x y^{2} sec^{2} (2 x y) d x

What is the limit as x approaches 0 of (sin(x))/(9x) ?
The limit as x approaches 0 of (sin(x))/(9x) is 1/9