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

 Calculus Calculus Math Forum

 November 10th, 2016, 05:19 PM #1 Member   Joined: Aug 2016 From: South Korea Posts: 55 Thanks: 0 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??
 November 10th, 2016, 05:45 PM #2 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Is this your question given? $\displaystyle \lim_{x\rightarrow 0} 3x^2+\frac{2x}{x}$ If this is the question given, then the answer is 2.
 November 11th, 2016, 03:28 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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. Thanks from SlayedByMath

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