December 7th, 2014, 06:51 PM  #1 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244  Confusing limits question
I was looking through a text book and found this question: Given that$$ \lim_{x\to2}\,\dfrac{f(x)  5}{x  2} = 3$$ Find$$ \lim_{x\to2}\,f(x)$$ I'm sure I'm missing something obvious here. I've tried looking at it as a derivative statement, but there is nothing to suggest that $f$ is differentiable at $x = 2$. I need someone else's view on this question. 
December 7th, 2014, 07:00 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,934 Thanks: 1128 Math Focus: Elementary mathematics and beyond 
In order for the limit to exist, the limit of f(x) as x approaches 2 must equal 5.
Last edited by greg1313; December 9th, 2014 at 07:37 AM. 
December 7th, 2014, 08:02 PM  #3 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Thanks for the help.


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