Using L Hospital's rule, evaluate :
lim
x →0(x² – Sin²x)/x^2​

0

Step-by-step explanation:

L Hospital's rule states that as long as u have the form

of infinity / infinity or 0/0 in general you can take its derivative to find the limit.

In this case as X tends to 0, the numerator tends to 0

Denominator will also tends to 0.

We have the 0 / 0 form, which means we can take the derivative for its numerator and denominator which gives

(2x - 2SinxCosx) / 2x | lim x -> 0

= (2x - Sin2x) / 2x | lim x -> 0

Based on this equation, as x tends to 0

both numerator and denominator tends to 0.

So we take its second derivative,

(2 - 2Cos2x) / 2

Now as x -> 0,

we will get (2 - 2)/2 = 0