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

The limit as x approaches 0 of (sin(x))/(3x) is 1/3

Popular >

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

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

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{3}

x^{3} + y^{3} = 7 x y, (2, - 4)

y = \frac{1}{x ^{2}}, (- 1, 1)

\int_{\frac{1}{5}}^{7} 12 x ln (5 x) d x

\int \frac{- 1}{1 + x ^{2}} d x

\frac{d}{d x} (\frac{ln ( 2 x )}{5 x})

What is the limit as x approaches 0 of (sin(x))/(3x) ?
The limit as x approaches 0 of (sin(x))/(3x) is 1/3