Question

f(x)=sin(x^2-2) find discontinuios

Answer 1

Classification of Discontinuity Points
All discontinuity points are divided into discontinuities of the first and second kind.

The function f (x) has a discontinuity of the first kind at x = a if
There exist left-hand limit and right-hand limit ;
These one-sided limits are finite.
Further there may be the following two options:
The right-hand limit and the left-hand limit are equal to each other:

Such a point is called a removable discontinuity.
The right-hand limit and the left-hand limit are unequal:

In this case the function f (x) has a jump discontinuity.
The function f (x) is said to have a discontinuity of the second kind (or a nonremovable or essential discontinuity) at x = a, if at least one of the one-sided limits either does not exist or is infinite.