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

The limit as x approaches 0 of (sin(x))/(6x) is 1/6

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

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

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{6}

y = 5 + 4 x^{2} - 2 x^{3}, (2, 5)

x^{^{''}} + a x = 0

16 y^{^{''}} + 24 y^{^{'}} + 9 y = 0

\int 6 r 4 - r^{2} d r

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

What is the limit as x approaches 0 of (sin(x))/(6x) ?
The limit as x approaches 0 of (sin(x))/(6x) is 1/6