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

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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}

\int x x + 9 d x

x \to - 1 lim (x^{2} - 5 x + 6)

\frac{\partial}{\partial y} (3 x^{2} - 3 y)

\int \frac{( x ^{2} - 9 )}{x ^{3}} d x

\frac{d}{d x} ((6 x + 5) (x^{3} - 2))

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