The limit of sin(x^2)/x as x approaches 0 is equal to 0. The lim_{x -> 0} sin(x^{2})/x formula is given by

$\lim\limits_{x \to 0} \dfrac{\sin x^2}{x}=0$.

Let us learn how to find the limit of sin x square divided by x when x tends to 0.

## Lim_{x → 0} sin(x^{2})/x

We have

$\lim\limits_{x \to 0} \dfrac{\sin x^2}{x}$

= $\lim\limits_{x \to 0} \dfrac{\sin x^2}{x^2} \times x$

= $\lim\limits_{x \to 0} \dfrac{\sin x^2}{x^2} \times \lim\limits_{x \to 0} x$ by the product rule of limits.

[Let x^{2}=t, so that t→0 as x→0]

= $\lim\limits_{t \to 0} \dfrac{\sin t}{t} \times \lim\limits_{x \to 0} x$

= 1 × 0 using the formula lim_{x→0} sinx/x =1.

= 0

So the limit of sin(x^{2})/x as x approaches 0 is equal to 0.

**More reading:** Limit of x/sinx when x→0

## Limit of sin(x^2)/2x as x→0

The given limit can be written as follows:

$\lim\limits_{x \to 0} \dfrac{\sin x^2}{2x}$

= $\dfrac{1}{2}\lim\limits_{x \to 0} \dfrac{\sin x^2}{x}$ as 1/2 is a constant.

= $\dfrac{1}{2}\times 0$ by the above limit formula.

= 0.

So the limit of sin(x^2)/2x as x→0 is equal to 0.

**Have You Read These Limits?** Limit of sin3x/sin2x when x→0

## FAQs

### Q1: What is the limit of sin(x^{2})/x when x→0?

Answer: The limit of sin(x^{2})/x when x→0 is equal to 0, that is, lim_{x→0} sin(x^{2})/x =0.