As I said, it is continuous wherever the denominator is nonzero. The denominator is zero at ##x=n\pi## where ##n## is any integer. The function is not even defined at these points, let alone continuous. It is defined and continuous everywhere else. Putting it another way, it is continuous on its domain.DrunkenPhD said:
The definition of continuity for a function is that it has no abrupt changes or breaks in its graph. This means that there are no gaps, holes, or jumps in the graph of the function.
To determine if a function is continuous at a specific point, you need to check if the limit of the function as x approaches that point is equal to the value of the function at that point. If these two values are equal, then the function is continuous at that point.
Point continuity refers to the continuity of a function at a specific point, as described in the definition of continuity. Interval continuity, on the other hand, refers to the continuity of a function over an interval of values, meaning that the function is continuous for all values within that interval.
No, a function is not always continuous if it is differentiable. A function can be differentiable at a specific point, but it may not be continuous at that point if there is a break or discontinuity in the graph.
Yes, it is possible for a function to be continuous at one point and discontinuous at another. This means that the function may have a break or discontinuity at one point, but is still continuous at other points along its graph.