More importantly are approach and equal the same as when we evaluate any limit we in end say that limit IS EQUAL TO some value , or there is no limit, but how can something APPROACHING is EQUAL TO SOMETHING . When we evaluate limit as x approaches zero , it is very similar to f(0), so why do we need limit st all.

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Actually if we do NOT say then it is equal to it then we cannot find the limit. And other things is that limit itself means that it is NOT the exact value of the function BUT is the value approaching from either side.