Sequence limit

Anonymous11

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Sep 21, 2017
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So there are given two sequences (xn)n>=1 and (yn)n>=1 of real and nonzero numbers which both converge to zero.
I have to calculate lim as x approches infinity of [(xn)2*yn]/ [3*(xn)2-2*xnyn+(yn)2].
(The first paranthesis is the numerator and the second one is the denominator.)
I tried to do it but I can't figure how I can prove it generally without using any specific sequence like 1/n .
Any ideas?
Thanks!
 
Last edited:
So there are given two sequences (xn)n>=1 and (yn)n>=1 of real and nonzero numbers which both converge to zero.
I have to calculate lim as x approches infinity of (xn)2*yn/3(xn)2-2xnyn+(yn)2..... something is missing here...
I tried to do it but I can't figure how I can prove it generally without using any specific sequence like 1/n .
Any ideas?
Thanks!
Is the expression you are investigating:

\(\displaystyle \displaystyle{(x_n)^2 * \frac{y_n}{3}(x_n)^2 - 2 * x_n*y_{n+}(y_n)^2}\) ..... this is what you wrote

or something else....

Please repost using proper grouping symbols.
 
Is the expression you are investigating:

\(\displaystyle \displaystyle{(x_n)^2 * \frac{y_n}{3}(x_n)^2 - 2 * x_n*y_{n+}(y_n)^2}\) ..... this is what you wrote

or something else....

Please repost using proper grouping symbols.

I edited it , I hope is clearer now.
 
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