Like what you saw?
Create FREE Account and:
- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics
Continuity - Problem 1FREE
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.
Stuck on a Math Problem?
Ask Genie for a step-by-step solution
Please enter your name.
Are you sure you want to delete this comment?