I am aware that for a function that is undefined at a point x=a such as [itex]f(x)=1/(x-a)[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]\underbrace{lim}_{x\rightarrow a}f(x)=\pm \infty[/tex]

But it tends to infinite only because it is in the form a/0, where a[itex]\neq[/itex]0.

Undefined values in the form 0/0 can have a range of values - all reals if I'm not mistaken.

I thus set up a function f(x) multiplied by another function g(x) so that f(a)=0 and g(a) undefined. However, the functions are not in a form where they can seemingly cancel factors of the zero and undefined value.

e.g.

[tex]h(x)=\frac{x+1}{x^2-1}=\frac{1}{x-1}, x\neq \pm 1[/tex]

So, such a function I simply came up with was

[tex]h(x)=x*tan(x+\frac{\pi}{2})[/tex]

I used a graphing calculator to try understand what was happening around x=0, and it seems that

[tex]\underbrace{lim}_{x\rightarrow 0}h(x)=-1[/tex]

Now I just want to understand why this limit tends to -1, not any other real values.

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# Undefined Points

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