I believe the expression you provided is:
(log(x) + 4x^3) / x
To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.
There are two types of discontinuities to look for:
Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.
Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.
To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.
So we solve the equation:
x = 0
This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.
Therefore, the only discontinuity of the expression is at x = 0.
Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.