Question about limits?

Question

I have a question about taking limits... I never know, when taking the limit as x approachs something like 0 or infinity, how to go about the problem... well obviously I try to rearrange the equations to see if anything cancels, but then I never know whether to try to take the limit as x approaches from either side, or whether to use l'Hopital's rule, or do something completely different... I just get confused...

Is there some kind of checklist of things to try (in order of how you should try them) when evaluating limits like this? By limits like this I really mean limits where you can't directly sub in the number (or other variable) that x approaches.... Thanks!

(and I know l'Hopital's rule is only for indeterminate equations or whatever those are called, I was just giving an example...)

Thanks again! :)

What I mean is, when the question just says "Evaluate the limit" and then it's some complicated function as x approaches something like 0, I don't really know what to try, without wasting a lot of time doing calculations that will lead me down the wrong path....

Answer 1

First of all, the question itself will tell you if you are supposed to take X to zero, to +infinity, or - infinity. It will also tell you, if it is supposed to approach zero from left, right, or both.

First thing I would try first, is a direct substitution. Sometimes, I can put ZERO into X and if it doesn't end up in invalid condition, such as divided by zero, you can arrive at limit that way.

Then, if it is supposed to be approaching zero or approaching certain number type problem, then, in order for a general limit to be present, it would have to approach the same value regardless of approaching from right or left. It they don't, general limit does not exist. Only one sided limit exists.

Then, if direct substitution cause you to end up in invalid condition, then factor them or somehow, eliminate the condition that will cause it. Then use direct substitution method on the simplified equation.

Your teacher should have explained all this in your class. You might want to go back and review your notes.

Answer 2

It's fairly simple.

When something approaches 0 you have to think of a small number like .0001 so any number multipled by this small number also approaches zero n x .0001(or 0). When any number divided by a number that approaches zero then that number goes to infinity. n /.0001

When a number goes to infinity then the inverse of number going to zero happens. Think of a large number like 10000.

n x 10000 or n/10000

You can cancel infinity and zero numbers in equations, but when you get them simplifyed then use the logic stated above.

Answer 3

you seem like you actually do know what you are doing, its just that every limit problems are approached differently.