is it ok that a Limit gives me 0 as answer? like... lim of x^2 - 4 when x->-2 = ?

Question

lim x^2 - 4
x->-2

would that just be 0? or I have to clear it in a such way that it doesnt gives me 0 as answer?

What if x->0 ? that gives me just zeros most of the times, is that ok too?

Answer 1

Yes, that's fine. Zero is the same as any other number. Now if you have 0/0, ∞/∞, ∞*0, 1^∞, 0^0, ∞-∞, or any other indeterminate form, then you would have to give additional considerations, but 0 is not itself indeterminate.

N.B. - many students seem to be confused about the difference between intederminate and undefined. Some indeterminate forms are perfectly well defined -- e.g. 0^0 is 1, and if you have the actual expression 0^0 and not f(x)^g(x) with both [x→0]lim f(x) = 0 and [x→0]lim g(x) = 0, you can evaluate it immediately as 1. Conversely, some undefined forms are not indeterminate: 1/0 is undefined, but not indeterminate, because limits of the form 1/0 ALWAYS diverge in some fashion (whether the limit is ∞, -∞, or undefined requires some inspection, but the limit cannot possibly be any finite value, such as 2).

Edit: "What if x->0 ? that gives me just zeros most of the times, is that ok too?"

Yes, that's fine. The indeterminate forms do not depend on what value x is approaching. Actually, if you read my orignal posting carefully, you will see that I accidentally wrote [x→0]lim f(x) instead of [x→-2]lim f(x), simply because I see limits as x→0 so much more often than limits as x→-2. But the rules for indeterminate forms are the same whether x approaches 0, -2, e, 75364, or any other number. And 0 by itself is never indeterminate.

Answer 2

1) limit of a function is a number... whatever number.
2) limit of x^2 - 4 when x goes to 2 is 0
when x goes to 0 is -4
when x goes to 5 is 21
3) the problem is when the number is not clear:
a) limit of sinx/x when x goes to 0 is 1
b) limit of (x^2 -1)/(x-1) when x goes to 1 is 2

in this case we can not put the number in the fraction because appears a thing that is not a number... is something that does not exist in Math... 0/0 . The mathematicians call this indeterminate form... it is not a number... and the result of the limit can be different, like example a) and b)

4) There are several kinds of indetermination... that above is of type 0/0

5) When the result is 0/5 it is the number 0. But, 5/0 is not a number... When this occurs in limit we say the limit is infinity... that means the limit does not exist(because limit is a number) but the function image is growing (up or down) without stopping.

Answer 3

Yes, zero can be the limit of an expression.

In your case:

limit (x -> -2) of [x^2-4]

is just [(-2)^2-4] or [4-4] or 0.

Answer 4

Just plain . I think you may be confusing this with problems where you get 0/0 which is undefined. In the case you need to use L'Hospitals rule.

Answer 5

It is 0. Try graphing it. 0/0 is what you have to watch out for.

Answer 6

Yes zero is fine if you want you since this is a continous function you can plug the point in and then you would have the answer of zero. You can only plug the number in if the function is one to one, continous and onto.

Answer 7

0 is fine as long as it's not on the bottom of a fraction.

Answer 8

no you dont have to modify anything....zero is fine, it's the correct answer:)