May 22nd, 2018, 04:49 AM  #1 
Member Joined: Jul 2017 From: KOLKATA Posts: 30 Thanks: 2  limit of Mod functions
lim x/x as x>infinity I Think this should be = 1 as this is indeterminate form and we can apply L Hospitals Rule . But the text book answer says that limit does not exist . which one is correct 
May 22nd, 2018, 05:09 AM  #2 
Senior Member Joined: Aug 2017 From: United Kingdom Posts: 270 Thanks: 81 Math Focus: Algebraic Number Theory, Arithmetic Geometry 
You're right that the limit as x tends to infinity is 1. (But you really don't need L'Hospital to see this. Just plot the graph of this function: it takes the value 1 for all x > 0 and the value 1 for all x < 0.) I suspect the book meant to ask about the limit as x tends to zero, in which case it's correct in saying there is no limit. Indeed, it has distinct left and right limits at 0 (1 and 1). 
May 22nd, 2018, 05:42 AM  #3 
Member Joined: Jul 2017 From: KOLKATA Posts: 30 Thanks: 2 
But since x tends to infinity x < 0 will not come into picture . So limit is always 1 . Am I correct ?

May 22nd, 2018, 05:44 AM  #4 
Member Joined: Jul 2017 From: KOLKATA Posts: 30 Thanks: 2 
I agree limit will not exist if x tends to 0

May 22nd, 2018, 06:11 AM  #5  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra  Quote:
Whenever dealing with $f(X)$, you first determine whether $f(x)=0$ zero within the interval of interest. If it does, split the interval at all such points and consider subintervals separately. Then for each (sub)interval simply replace $f(x)$ with either $f(x)$ or $f(x)$ as appropriate.  

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