Question

I will give BRAINLIEST.

If x4≤f(x)≤x2 for x in ​[−​1,1] and x2≤f(x)≤x4 for x<−1 and x>​1, at what points c do you automatically know limx→c f(x)​? What can you say about the value of the limit at these​ points?

Answer 1

You would know that

$\displaystyle\lim_{x\to\pm1}f(x)=1$

It follows from the sandwich/squeeze theorem: for instance,

$x^4 \le f(x) \le x^2 \implies \displaystyle\lim_{x\to-1}x^4 \le \lim_{x\to-1}f(x) \le \lim_{x\to-1}x^2 \implies 1 \le \lim_{x\to-1}f(x) \le 1 \\\\ \implies \lim_{x\to-1}f(x)=1$