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Suppose that f : [0; 1] ! R is increasing on [0; 1] and that 0...

Suppose that f : [0; 1] ! R is increasing on [0; 1] and that 0 < a < 1. Prove that limx!a? f(x)
exists.

Math   Calculus   
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Answer #1

So, this directly proves that as this function gradually increases therefore at any point between x=(0,1) the limit exists for sure, as limit at a (ie. Between 0 and 1) exists !!

Not at x={0} and not at x={1} since the Left Hand limit at x=0 and Right Hand limit at x=1 is not defined.

But in between those numbers, the limit always exists.

Hence, proved !!

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