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

The limit as x approaches 0 of sin(x) is 0

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limit as x approaches 0 of sin(x)

x \to 0 lim (sin (x))

0

Solution steps

x \to 0 lim (sin (x))

Plug in the value

x = 0

= sin (0)

Use the following trivial identity:

sin (0) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

\int \frac{1}{x y} d x

\frac{\partial}{\partial r} (e^{r} cos (t))

x^{2} (\frac{d y}{d x}) - x y + 3 y^{2} = 0

\int_{0}^{2} x^{3} x^{2} + 4 d x

\frac{\partial}{\partial y} (4 y - 3 x^{2})

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