Limit of sin(x^2)/x as x approaches 0

The limit of sin(x^2)/x as x approaches 0 is equal to 0. The lim_{x -> 0} sin(x²)/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(x²)/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 x²=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(x²)/x as x approaches 0 is equal to 0.

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

Limit of sinx/x when x→∞

Limit of sin(1/x) 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

Limit of tanx/x when x→0

Limx→0 (cosx-1)/x	Limx→0 (ax-1)/x
Limx→0(ex-1)/x	Limx→0 log(1+x)/x

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