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-   -   Help!! How do I find table of values for undetermined Limit? (http://mymathforum.com/calculus/337283-help-how-do-i-find-table-values-undetermined-limit.html)

 SlayedByMath November 10th, 2016 05:19 PM

Help!! How do I find table of values for undetermined Limit?

The given problem is 3x^2 + 2x/x , x> 0

and the only ans. Ive got is 0/0

How do I make Table of values for this and how can I determine if the limit exists or not??

 jiasyuen November 10th, 2016 05:45 PM

$\displaystyle \lim_{x\rightarrow 0} 3x^2+\frac{2x}{x}$

If this is the question given, then the answer is 2.

 Country Boy November 11th, 2016 03:28 AM

By "table of values", I think you mean just a table of values of your function for x close to 0.

If you mean $3x^2+ \frac{2x}{x}$ as jiasyuen suggested (which is what you wrote) then when
x= 1, y= 3+ 2/2= 4
x= 1/2, y= (3/4)+ 1/(1/2)= 2.75
x= 1/4, y= (3/16)+ (1/2)/(1/4)= 2.1875
etc.

If you mean, as I suspect, [tex]\frac{3x^2+ 2x}{x} then
x= 1, y= (3+ 2)/1= 5
x= 1/2, y= (3/4+ 1)/1/2= 2(7/4)= 7/2= 3.5
x= 1/4, y= (3/16+ 1/2)/(1/4)= 4(11/16)= 11/4= 2.75
x= 1/8, y= (3/64+ 1/4)(1/8 )= 8(19/64)= 9/8= 1.125
etc.

You don't have to choose one over powers of two- that was my choice. Just a sequence of number getting closer and closer to 0.

But you really should not have to look at numbers like that- for one thing there exist functions such that you can get "closer and closer" to what looks like a limit but then, when you are really close, suddenly change.

Instead use the fact that $\frac{3x^2+ 2x}{x}= \frac{(3x+ 2)x}{x}$ and, as long as x is not 0, those 'x's cancel: $\frac{(3x+ 2)x}{x}= 3x+ 2$.
The limit, as x goes to 0, is 3(0)+ 2= 2.

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