What are continuity and limits in calculus?

Can you explain what continuity means in calculus?

Continuity in calculus refers to a function being continuous at a point if the limit as you approach that point equals the function's value at that point.

What about limits? How do they relate to continuity?

Limits describe the behavior of a function as it approaches a certain point. A function is continuous if the limit at that point exists and equals the function's value.

Can you give me an example of a function that is not continuous?

Sure! The function f(x) = 1/x is not continuous at x = 0 because it approaches infinity as x approaches 0, and f(0) is undefined.

How do you determine if a function is continuous at a point?

To determine continuity at a point, check three conditions: the function must be defined at that point, the limit must exist, and the limit must equal the function's value.