MarkFL said:To ensure continuity, we require:
\(\displaystyle \lim_{x\to-2}\frac{x^2-4}{x+2}=4\)
Is this true?
kendalgenevieve said:I just got -4 so no it does not equal 4
Continuity is a property of a function where the output values of the function change gradually as the input values change. In other words, there are no sudden jumps or breaks in the graph of the function.
A function is continuous at a specific point if the limit of the function at that point exists and is equal to the value of the function at that point. In other words, as the input values approach the specific point, the output values also approach the same value.
Yes, a function can be continuous at one point but not continuous at another. This is because continuity is a local property, meaning it is determined at a specific point and does not necessarily apply to the entire function.
Polynomial functions, rational functions, exponential functions, and trigonometric functions are always continuous. This means that they are continuous at every point in their domain.
If a function is continuous at a point, it does not necessarily mean that it is differentiable at that point. However, if a function is differentiable at a point, it must also be continuous at that point.