I am trying to fully understand this example from a textbook I am reading:(adsbygoogle = window.adsbygoogle || []).push({});

http://img59.imageshack.us/img59/9237/continuityyn8.jpg [Broken]

What I am not understanding is how they are proving it for [-1,1].. The way I see it is they proved that the function is continuous for all values in it's domain...

For example, I thought up this problem on my own to help me understand :

Given [tex] f(x)=1-\frac{1}{x-4} [/tex], prove that f(x) is continuous in the interval [-1,30] (Obviously it's not continuous at x=4.) The problem is that I don't see the connection between the interval and the solution...

I can just go ahead and prove that [tex]\lim_{x\rightarrow a}f(x)=f(a)[/tex]... Which was stated in my text as meaning that the function is continuous... which it obviously isnt.

[tex]\lim_{x\rightarrow a}f(x)=\lim_{x\rightarrow a}(1-\frac{1}{x-4})[/tex]

[tex]=1-\lim_{x\rightarrow a}\frac{1}{x-4}[/tex]

[tex]=1-\frac{1}{a-4}[/tex]

[tex]=f(a)[/tex]

Can someone cure my confusion? Thanks guys.

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# Proving continuity

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