Find limit X approaches 1 for

((5-X)^.5 -2)/((2-X)^.5 -1)

e-mail address: mark.hultgren

Thank you.

2 answers

Substitute x = 1 - t and expand the squareroots in series using the formula:

sqrt[1 + y] = 1 + y/2 + O(y^2)

You should then find that the limit is 1/2
or

Multiply by ((5-X)^.5 + 2)/((5-X)^.5 + 2)*((2-X)^.5 + 1)/((2-X)^.5 + 1)
which reduces your question to
Limit ((2-X)^.5 + 1)/((5-X)^.5 + 2) as x-->1
= 2/4
= 1/2

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