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0/0 DNE or undefined? 
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#1
Apr2914, 04:46 AM

P: 819

What can we deduce about the lim g(x,y) as (x,y) > (0,0)?
where g(x,y) = sin(x)/x+y in substituiting, we get 0/0 so it has an indeterminate form which requires further work to ascertain if it is truly DNE or if it has a limit. What I've been hearing too is that since it is 0/0 for the above function, the limit DNE. Which is which? Or are definitions being loosely used? 


#2
Apr2914, 05:34 AM

Sci Advisor
P: 827

Is that ##\frac{\sin(x)}{x} + y## or ##\frac{\sin(x)}{x+y}##?



#3
Apr2914, 06:17 AM

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#4
Apr2914, 06:43 AM

P: 819

0/0 DNE or undefined?
From my notes, it reads " the limiting behaviour is path dependent so lim of the function g(x,y) as (x,y) >0 does not exists. 


#5
Apr2914, 06:43 AM

P: 819

Edit: sorry, latter! The former has a limit by performing l'hopital rule. 


#6
Apr2914, 09:10 AM

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This can happen even in one dimension. What's the derivative of x at x=0? 


#7
Apr2914, 09:33 AM

P: 819




#8
Apr2914, 09:40 AM

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P: 15,155

Precisely. The onesided limits ##\lim_{h \to 0^+} \frac{x+h  x}{h}## and ##\lim_{h \to 0^} \frac{x+h  x}{h}## exist at x=0 but differ from one another. Therefore the twosided limit ##\lim_{h \to 0} \frac{x+h  x}{h}## doesn't exist at x=0.



#9
Apr2914, 09:50 AM

P: 819




#10
Apr2914, 10:29 AM

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P: 15,155

Continuity and limits go hand in hand. A function f(x) is continuous at some point x=a if



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