My Math Forum limit of Mod functions

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 May 22nd, 2018, 05:49 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, 06:09 AM #2 Senior Member   Joined: Aug 2017 From: United Kingdom Posts: 307 Thanks: 101 Math Focus: Number Theory, Algebraic 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, 06:42 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, 06:44 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, 07:11 AM   #5
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Quote:
 Originally Posted by arybhatta01 But since x tends to infinity x < 0 will not come into picture . So limit is always 1 . Am I correct ?
Yes.

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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