In simple words, in the left side what's the limit? in the right one, what's the limit? are those equal? if so, then the limit of the squeezed function is the same.
If sqrt(5-2x^2) <= f(x) <= sqrt(5-x^2) for -1 <= x <= 1, find limit f(x) as x goes to 0.
What exactly is the first step in doing these types of problems? This theorem is the only one that I have trouble with as I missed the day of class when we were discussing it.
<= is less than or equal to. I guess I will have to find the latex codes for these problems.
you do have to check if the left side limit is equal to the right side. if they are the same, limit of f(x) will also be the same.
we can see that,
limit of sqrt(5-2x^2) = sqrt 5 when x tends to 0
limit of sqrt(5-x^2) = sqrt 5 when x tends to 0
Hence from here, we can conclude that
limit of f(x) = sqrt 5 when x tends to 0