Calculus Review Help? Discontinuity
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Calculus Review Help? Discontinuity

[From: ] [author: ] [Date: 13-02-24] [Hit: ]
Try graphing the function and you should notice a little hole, even if it would be possible to simply cancel them out.It is also discontinuous at x = 2.-Its discontinuous for x values that make the denominator zero.HOWEVER: if you can cancel something out thats in the numerator and denominator, that doesnt count.......
Let g(x) =(x-2)^2/x(x-2)
Give all x-values for which g is discontinuous?

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Paul was correct about most points, except the canceling out. While it may not be what you're use to, you still get a hole discontinuity at these points. Try graphing the function and you should notice a little hole, even if it would be possible to simply cancel them out.4

It is also discontinuous at x = 2.

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It's discontinuous for x values that make the denominator zero. HOWEVER: if you can cancel something out that's in the numerator and denominator, that doesn't count. So in this case you can simplify your equation to (x-2)/x. That means it's only discontinuous when x=0.
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