limit writing assignment

[livelaughlovee]

help please! i don't even know where to start...

here's what I have to do:

 

[mmm4444bot]

(I'd swear that I already replied to this post several minutes ago. :? )

What do you know about limits?

I mean, this is where to start: the meaning of a limit.

Tell me what a limit means to you, in your own words, and we'll go from there.

(To me, this exercise has a tricky component because of several sloppy educators and textbook authors.)

 

[BigGlenntheHeavy]

The existence of a limit.

Theorem: If f is a function and c and L are real numbers, then the limit of f(x) as x approaches c is L if and only if:

\(\displaystyle \lim_{x\to c^{-}}f(x) \ = \ L \ and \ \lim_{x\to c^{+}}f(x) \ = \ L.\)

Now, in your above thread, is L a real number?, no because infinity is not a real number, hence the limit doesn't exist for either function..

\(\displaystyle \lim_{x\to2^{-}}\frac{1}{x-2} \ = \ -\infty, \ and \ \lim_{x\to2^{+}}\frac{1}{x-2} \ = \ \infty.\)

[attachment=1:jmvdnhod]abc.jpg[/attachment:jmvdnhod]

\(\displaystyle \lim_{x\to2^{-}}\frac{1}{(x-2)^{2}} \ = \ \infty \ and \ \lim_{x\to2^{+}}\frac{1}{(x-2)^{2}} \ = \ \infty.\)

[attachment=0:jmvdnhod]def.jpg[/attachment:jmvdnhod]

 

[Deleted member 4993]

Re:

(I'd swear that I already replied to this post several minutes ago. :? )

You probably previwed it and forgot to "submit" it - I have done that several times (only 25% quota used)

 

[mmm4444bot]

You probably previwed it and forgot to "submit" it …

That definitely sounds plausible, but I'd rather blame it on Microsoft and the tens of thousands of documented, unresolved bugs in their software products. :x