Question

How do I solve this! Calc, please help! Suppose that a function f(x) is defined for all x in [-1,1]. Can anything be said about the existence of lim x->0 f(x)? Give reasons

Answer 1

Well, I suppose if \(f(x)\) is defined for all \(x\) in the interval \([a,b]\) and there exists an x-value, \(h\) in the same interval, then:
\[\lim_{x\to h}f(x)\textit{ exists}\]

Answer 2

So if our interval is \([-1,1]\) and for sure there exists the number zero in that interval, then:
\[\lim_{x\to0}f(x)\textit{ exists}\]

Answer 3

What is the reasoning for this, just that logically the defined limit of 0 falls within the borders of [-1.1]?