find points of discontinuity; state condition violated

[mika0]

9. Find at least one point at which each function is not continuous and state which of the three conditions in the definition of continuity is violated at that point.

\(\displaystyle \mbox{(a) }\, \dfrac{x\, +\, 5}{x\, -\, 3}\). . . . .\(\displaystyle \mbox{(b) }\, \dfrac{x^2\, +\, x\, -\, 6}{x\, -\, 2}\). . . . .\(\displaystyle \mbox{(c) }\, \dfrac{x}{x}\)

\(\displaystyle \mbox{(d) }\, \dfrac{\pi}{x^2\, -\, 6x\,+\, 9}\). . . . .\(\displaystyle \mbox{(e) }\, \ln(x^2)\)

I can't solve this,please just solve one of them for example and I'll do the others

 

[Deleted member 4993]

9. Find at least one point at which each function is not continuous and state which of the three conditions in the definition of continuity is violated at that point.

\(\displaystyle \mbox{(a) }\, \dfrac{x\, +\, 5}{x\, -\, 3}\). . . . .\(\displaystyle \mbox{(b) }\, \dfrac{x^2\, +\, x\, -\, 6}{x\, -\, 2}\). . . . .\(\displaystyle \mbox{(c) }\, \dfrac{x}{x}\)

\(\displaystyle \mbox{(d) }\, \dfrac{\pi}{x^2\, -\, 6x\,+\, 9}\). . . . .\(\displaystyle \mbox{(e) }\, \ln(x^2)\)

I can't solve this,please just solve one of them for example and I'll do the others

What are those three conditions of continuity?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions. Do you know the definition of functor? Where is it used?

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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[stapel]

9. Find at least one point at which each function is not continuous and state which of the three conditions in the definition of continuity is violated at that point.

\(\displaystyle \mbox{(a) }\, \dfrac{x\, +\, 5}{x\, -\, 3}\). . . . .\(\displaystyle \mbox{(b) }\, \dfrac{x^2\, +\, x\, -\, 6}{x\, -\, 2}\). . . . .\(\displaystyle \mbox{(c) }\, \dfrac{x}{x}\)

\(\displaystyle \mbox{(d) }\, \dfrac{\pi}{x^2\, -\, 6x\,+\, 9}\). . . . .\(\displaystyle \mbox{(e) }\, \ln(x^2)\)

I can't solve this,please just solve one of them for example and I'll do the others

Try using what you learned back in algebra about division by zero, vertical asymptotes, and the definition of logarithms.

 

[stapel]

1)when f(x)=0
2)derivative=0
3)how to solve it by log?I dont know

How do these numbered statements relate to the original post?