00:01
The objective is to evaluate the limit of sine inverse of 2x divided by x when x tends to 0.
00:11
Observe that if we substitute x is equal to 0 in this expression, it will be of the form 0 by 0.
00:19
So we need to use the alhorbital rule.
00:23
In al -habitol rule, if we have two functions say f of x divided by g of x and if the limit of this expression when x tends to some k becomes 0 by 0 or any other undefined forms, then we need to compute the ratio f dash of x divided by g dash of x, where f dash of x and g dash of x are nothing but the derivatives of f of x and g of x.
00:52
Now we need to compute the limit of this expression when x tends to the same number k.
00:59
If this number exists, then we can say that the required limit is nothing but the limit what we have found here.
01:09
If we compare this expression with the given expression, we can understand that in our case, f of x is equal to sine inverse of 2x and g of x is equal to x, k is equal to 0.
01:26
So we need to find the value of f dash of x and g dash of x to use the l hobbit.
01:33
Rule.
01:34
If we differentiate sine inverse of 2x with respect to x, we will get 1 divided by root of 1 minus 2x the whole square, which is nothing but 4x square, times the derivative of 2x, which is nothing but 2.
01:51
So f dash of x can be written as 2 divided by root of 1 minus 4x square...