Limit X help

  • Thread starter jinbaw
  • Start date
  • #1
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Homework Statement



[tex] X \geq Y > 0, find \lim_{n \to \infty} \left(\frac{2X^n + 7Y^n}{2}\right)^{1/n}
[/tex]

Homework Equations





The Attempt at a Solution


I'm not really sure how to do it, but i guess I need to use the fact that [tex] \frac{Y}{X} \leq 1 [/tex], and so [tex] \lim_{n \to \infty} \left(\frac{Y}{X}\right)^n = 0. [/tex]
Thanks for your help.
 

Answers and Replies

  • #2
Cyosis
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Multiply the argument by [tex]\frac{X^n}{X^n}[/tex] then take the [tex]X^n[/tex] out of the brackets.
 
  • #3
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[tex] \lim_{n \to \infty} X \left( 1 + \left( \frac{7Y}{2X} \right)^n \right)^{1/n} [/tex]
But I'm still stuck on how to procceed, if you could help.
 
  • #4
Cyosis
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There is one mistake, 7/2 should not be within the brackets. Now take X in front of the limit and use [tex] \frac{Y}{X} \leq 1 \Rightarrow \lim_{n \to \infty} \left(\frac{Y}{X}\right)^n = 0[/tex].
 
  • #5
65
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Oh right.. So its limit is X.
Thanks :-D
 
  • #6
Cyosis
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That's right!
 

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