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Finding limit- greatest integer function

  1. Nov 14, 2011 #1
    Hi, I was studying for my upcoming calculus exam and couldn't be sure if I could solve this question:

    [itex]\stackrel{lim}{x\rightarrow0}[/itex] x [[itex]\frac{1}{x}[/itex] ]

    If x approaches 0 from left, then 0< x [[itex]\frac{1}{x}[/itex] ]<1

    If x approaches 0 from right, then x [[itex]\frac{1}{x}[/itex] ]>1 since x [[itex]\frac{1}{x}[/itex] ]=[itex]\frac{x}{x-1}[/itex]

    Hence, the limit is equal to 1.

    Is this solution true? Thank you for any help :)
     
  2. jcsd
  3. Nov 14, 2011 #2
    we know that t-1< [t] <= t.
    Replace here t by 1/x.
    I think your answer is correct.This form of inequality is more formal method.
     
  4. Nov 14, 2011 #3
    Thanks, Bhaskar. You're right, I should be able to write it formally.
     
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