0
An intuitive answer (NOTE: this is far from precise!)
A function is continuous if you can trace its graph without lifting your pencil from the page. If, additionally, it is smooth everywhere without any jagged edges or abrupt corners, then it is differentiable. It is not possible for a function to be differentiable but not continuous. On the other hand, plenty of functions are continuous without being differentiable.
Still curious? Ask our experts.
Chat with our AI personalities
Beau
Rene
BlakeAdd your answer:
Earn +20 pts
What is the difference between tangent continuity and curvature continuity?
Tangent continuity: No sharp angles. Curvature continuity: No sharp radius changes.
What is the definition of continuity of the function and how do you determine a function is continuous?
There are several different ways of defining continuity. The following is based on work done by Bolzano and Weierstrass.A function f(x), of a variable x is continuous at the point c if, given any positive number e, however small, it is possible to find d such thatf(c) - e < f(c) < f(c) + efor ALL x in c - d < x < c + d.In simpler terms, it is possible to find an interval around x such that for ALL values of x' in that interval, the value of the function, f(x'), is close to f(x).Determining continuity visually, it is easy: if the function can be drawn without lifting your pencil, then it is continuous and if you cannot, it is not.
What are the rules of continuity of a graph?
If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".
What are the answers for IS-547a Introduction to Continuity?
responses is 547.a Introduction to Continuity
What is the conditional expectation function?
It is the integral (or sum) of the joint probability distribution function of the two events, integrated over the domain in which the condition is met.
