### Learn math, science, English SAT & ACT from

high-quaility study
videos by expert teachers

##### Thank you for watching the preview.

To unlock all 5,300 videos, start your free trial.

# Continuity - Problem 1

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

To check if a function is continuous at a point, first check if the function exists at that point (if for that x, there exists an f(x)). Then, check if the limit as x approaches that point exists. Recall that this can be done by checking if the left- and right-hand limits are the same. Finally, for a function to be continuous, the value of the function at a point must be the same as the limit of the function at that point.

Let's take a look at an example. We have this function graphed here y equals f(x). I want to know why this function is not continuous at x equals -2 right here.

Well, remember that there are three conditions for continuity. The function has to be defined at the number in question. The limit as x approaches that number f(x) has to exist. Finally, that limit has to equal the value of the function at that number.

Now the number here is -2. Our problem is with the first condition f(a) doesn't exist. F(-2) does not exist. It is not defined. So the function is not continuous at -2.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

##### Concept (1)

##### Sample Problems (3)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete