Continuity of a function means that the function has no abrupt changes or breaks in its graph. In other words, the graph of a continuous function can be drawn without lifting your pencil.
To find the values of p and q, we need to use the definition of continuity. This means that the limit of the function as x approaches the point of interest must be equal to the value of the function at that point.
Yes, a function can be continuous at a single point. This means that the limit of the function exists and is equal to the value of the function at that point.
Yes, it is possible for a function to have multiple values for p and q that make it continuous. This is because there are often multiple ways to approach a point and make the limit equal to the value of the function at that point.
It is important to find the values of p and q that make a function continuous because continuous functions have many applications in mathematics and the sciences. They are used to model real-world situations and make predictions based on data. Additionally, continuity is a fundamental concept in calculus and is necessary for solving many problems involving derivatives and integrals.