Is there a website or can someone who help me with finding a limit-calculus? Thanks?
Example: find lim (x arrow pointing at 2 under lim) g(x), where g(x)=2^2+4/x-2
Sorry I did write it wrong. It is suppose to be:
Find lim x-->2 g(x), where g(x)=(x^2+4)/(x-2).
I did it wrong again. I don't know what is wrong with me. I am looking at the problem and typing something different. One more time:
Find lim x-->2 g(x), where g(x)=(x^2+4)/(x-2)
- 1 decade agoFavorite Answer
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- Joni DaNerdLv 61 decade ago
Um... i just saw your example, are you missing some variables and/or parenthesis?
The lim with the x arrow pointing at 2 is ok, I get your meaing there. But the way you have it written, do you mean 2^2 + (4/x) -2?
In that case, simply substitute the 2 and you get 4 + (4/2) -2 = 4 + 2 -2 = 4
Or do you mean 2^2 + 4/(x-2)?
In that case you get 4 + 4/0, which is infinite or undefined. (graph it and you'll see a vertical asymptote at 2, with the graph going to positive infinity on the right side of the asymptote and negative infinity on the left side.)
Or is there supposed to be an x with the 2, did you mean (2x^2 + 4)/(x-2)?
In that case, you still have a vertical asymptote with the function going to negative infintiy on the left side of 2 and positive infinity on the right, but the effect is more pronounced because of the square in the numerator.
When in doubt, use parenthesis.
Ok, I just saw your editing, and that still has a vertical asymptote at 2 and behaves similar to the other functions discussed here. So the answer is still limit undefined.
Generally, what you do with these is, you try and factor the numerator and denominator and cancel out common factors. If you can do this, you have what is called a "removable discontinuity" and so you can find a limit. Otherwise you have a "non removable discontinuity", which shows up as a vertical asymptote on the graph, and there's no limit.
Now if you'd had x^2 - 4 in the numerator you would have been able to remove the discontinuity. but with x^2 + 4 in the numerator, you're stuck with it.
- 1 decade ago
lim (x --> 2) (2*2 + 4/(x-2))
In this case is a simple limit: you just have to think what happens if x is close to 2, and continue reasoning based on it.
First of all, if x --> 2, then (x-2) --> 0
so, 4/(x-2) --> 4/0, e.g. infinite
if x > 2, then (x-2) is positive and so the limit is +infinite
if x < 2, then (x-2) is negative and so the limit is -infinite
the extra 2*2 added to +infinite or -infinite has no effect, so we are finished.
The conclusion is:
if x --> 2 "by the left" (e.g. with x < 2), then the limit is -infinite
if x --> 2 "by the right" (e.g. with x > 2), then the limit is +infinite
if, in general, we just know that x --> 2, then we cannot give any limite (because it is not clear if is +infinite or -infinite), and so the conclusion is that the limite DOES NOT EXIST.