Find all possible values of $y$ such that $$|\lim\limits_{x\rightarrow\infty}\frac{x^{1-y}}{x^{y}}|<\infty$$

  • 2
    $\begingroup$ the given expression is $x^{1-2y}$ so $y$ can be bigger than $1/2$. $\endgroup$
    – Anurag A
    Dec 21, 2019 at 9:26
  • $\begingroup$ How does the limit of $x^\alpha$ when $x\to\infty$ depend on the parameter $\alpha$ $\endgroup$
    – marwalix
    Dec 21, 2019 at 9:28

1 Answer 1


We can rewrite it as $|\lim_{x\to \infty} x^{1-2y}|$ and this limit is clearly less than infinity only when $1-2y≤0$. If $y>1/2$ the limit is zero and if $y=1/2$ the limit is $1$.


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