Expert: Paul Klarreich - 10/11/2011

Question
lim x->0(x/x)=1. What will happen when I do like this...lim x->0(x)lim x->0(1/x)=?( Is the answer 1 or any other) Every limit must follow its rule... Right? Please tell me what the stuff is going on....

Answer
Questioner:shameem
Country:India
Category:Calculus
Private:No
Subject:Limits tending to infinity

Question:

lim x->0(x/x)=1.

BECAUSE:
lim x->0(x/x) =

lim x->0 (1)

= 1

Next week your teacher will do continuity and use this example.
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What will happen when I do like this...lim x->0(x)lim x->0(1/x)=?( Is the answer 1 or any other)

WHAT will happen is you will not get any sensible answer.
....................................

Every limit must follow its rule... Right?

THAT sentence is meaningless.

Please tell me what the stuff is going on....

WHAT is going on is:  Lim(x->a) f(x) has nothing to do with  f(a), which does not have to exist.