Hello, I need some help with this
I need to find the limit of lim x->-2 2-|x| / 2+x
I need to evaluate the left and right handed limit. For the righthanded limit I plug in
lim -2+ 2-(x)/2+x,
now my problem is is to get something that can cancel out, so that I got the limit.
The lefthanded limit I did as following:
lim -2- 2-(-x)/2+x = lim -2- 2+x/2+x = 1
Thanks for any hint.
Because the limit is only related to the values near -2, that is to say the value between is totally meaningless. So you can just consider the case when .
Or you can refer the definition of the limit:
. In this way, you may understand the "limit"better.
Since if satisfy the definition for some , then any also satisfy the definition. So the limit is only related to the values near -2.
Thanks, I guess I was thinking in the wrong way. It took me a while to understand, but I guess what I did wrong was indeed not to see that in both cases x is smaller than zero and so I get 2+x in bith numerators.
I am still not sure if I understood the definition of the limit, because I do not know all these characters but I understand the problem to get an answer.