Thread: Problems with continuity

For some reason I'm having a heck of a time with Continuity. I'm self teaching myself calculus and have been doing very well except for continuity. The example and lessons in the book im using are just horrible. Below are some example problems I need help with. I think if I could see some actual examples worked out it would help as the book provided none!

Find Values of X, if any at which f is not continuous

f(x)=5x^4-3X+7 - would I use intermediate theorem on this one?

f(x)=X+2/X^2+4 - would I set the denominator to zero?

f(x)=3/x+x-1/x^2-1 - not a clue

Originally Posted by dan87951

For some reason I'm having a heck of a time with Continuity. I'm self teaching myself calculus and have been doing very well except for continuity. The example and lessons in the book im using are just horrible. Below are some example problems I need help with. I think if I could see some actual examples worked out it would help as the book provided none!

Find Values of X, if any at which f is not continuous

f(x)=5x^4-3X+7 - would I use intermediate theorem on this one?

f(x)=X+2/X^2+4 - would I set the denominator to zero?

f(x)=3/x+x-1/x^2-1 - not a clue

Keep in mind the fact that polynomial functions are continuous everywhere, and rational functions are continuous where they are defined. So the first function is continuous everywhere. The second and third functions are continuous where they are defined.

Do you understand how to find the domain of this function? If so, then determining the where the function is discontinuous should be pretty easy. This function is discontinuous at x=0,1, and -1, because these are the points on the x-axis where the function is not defined.

Yea I know how to find the domain. Just factor the bottom polynominal or what ever makes it 0 out.

My book doesn't saying anything about polynomials being continuous everywhere. Is there a website with more info on this? Or maybe someone can help me explain why. Is it because there is nothing to divide by that would make it undefined?

for f(x)=X+2/X^2+4 is it continuous everywhere except at X=2, -2?

and the last one that adkinsjr did means its continuous everywhere except at 0, 1, -1. Correct?

If what im understanding is correct. All I need to do is find the domain to see where its discontinuous?

BUMP..

Is what I have above safe to assume than?