Question

Find the numbers at which f is discontinuous.

f(x)= 1+x^2 if x<=0
2−x if 02

Answer 1

the left and right limits have different values at x=0

Answer 2

A function f(x) is said to be continuous at a point x = a iff

i). f(a) is defined
ii).\[\lim_{x \rightarrow a}f(x)\]exists
iii).\[\lim_{x \rightarrow a}f(x)=f(a)\]

If any of these conditions are not satisfied then we say that the function f(x) is discontinuous at x = a.


If a function f(x) is discontinuous at x = a, then it may have one of the following types of discontinuities.

Answer 3

@ConDawg let me know if you understand what I wrote.

Answer 4

okay I understand

Answer 5

So then try your question and I'll check it.

Answer 6

I started to write the rest of the lesson as you can see but then decided not to at the moment because to answer your question this should be sufficient for now. If needed I will tell you about the different types of discontinuities such as jump, removable, and infinite discontinuities later.

Answer 7

No its okay im watching a youtube video about the types of discontinuities

Answer 8

OK! So I guess that's a polite way of saying that my help is not wanted. lol

Answer 9

No thats not what I meant I thought I would save you the time, but you help is needed, I dont know how I should go about and do this. if you gave me an example I think that would help a lot

Answer 10

Example:
Examine the continuity of the following function for continuity:

Looking at the restrictions, we see that here we have two x = a values. x = 0 and x = 1.
Thus we check for continuity for each of these.

For x = 0,
i). f(0) is undefined.

Thus f(x) is discontinuous at x = 0


For x = 1,


Thus f(x) is discontinuous at x = 1.

∴ f(x0 is continuous at x = 1 and f(x) is discontinuous at x = 0.