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March 26, 2017

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Find limit X approaches 1 for
((5-X)^.5 -2)/((2-X)^.5 -1)

e-mail address: mark.hultgren@ca.usda.gov

Thank you.

  • college - ,

    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

  • college - ,

    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

    BTW, it is strongly suggested that you do not put your email or personal information in these postings

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