Finding limit- greatest integer function

  • #1

Main Question or Discussion Point

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 :)
 

Answers and Replies

  • #2
134
0
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.
 
  • #3
Thanks, Bhaskar. You're right, I should be able to write it formally.
 

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