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Anyone knows about limitation and continuity?

Anyone knows about limitation and continuity?-example-1

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If you just plug x=1 in the expression, you can see that, as x approaches 1, the whole expression approaches the following quantity:



(√(1-y)-2)/(2-1) = (√(1-y)-2)/(1) = √(1-y)-2


Now, how can we find the value of y? We need some additional request. For example, if we knew that this limit had to equal 3, then we would have written



√(1-y)-2 = 3


and solved for y. But without something like this, we can only compute the limit and get rid of x, but y stays.

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