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Math Help - How can i solve this limit without using L'hospital's rule?

  1. #1
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    How can i solve this limit without using L'hospital's rule?

    How can i solve this limit without using L'hospital's rule?

    Limit[(2 - Sqrt[x + 1])/(x - 3), x -> 3]
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  2. #2
    MHF Contributor Calculus26's Avatar
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    multiply top and bottom by sqrt(x+1)

    you should get -(x-3)/[(x-3)sqrt(x+1)]
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    multiply top and bottom by sqrt(x+1)

    you should get -(x-3)/[(x-3)sqrt(x+1)]
    Don't u mean top and bottom by 2 + sqrt(x+1).
    And the problem is that after I solve that I get:
    -(x-3)/[(x-3)(2 + sqrt(x+1)]
    And when the limit is taken, it gives 0
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  4. #4
    MHF Contributor Calculus26's Avatar
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    yes multiply top and bottom by 2 +sqrt(x+1)

    then you get -1/[2+sqrt(x+1)]


    and lim -1/[2+sqrt(x+1)] = -1/3 not 0
    x->0
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  5. #5
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    Oh, I see where my error was, how embarrasing.
    Thanks so much
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