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I have $ f(x)=\frac{x*arctgx}{\sqrt{4x+3}} $ And $ g(x)=\sqrt x - {x}^{1/3} $

Limits of both functions are infinity, so these functions are infinitely large .

I need to write equivalent functions for both as $ C{x}^{n} $ and find out order of growth/smallness of functions and then compare f(x) and g(x).

I don't no how to write equivalent for f(x) and what are common ideas of tasks like this, in my lecture copybook I didn't find anything/

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$f(x)=x^{1/2} \frac {\arctan (x)} {\sqrt {4+\frac 3 x}}$ and $g(x)=x^{1/2} (1-x^{\frac 1 3 -\frac 1 2})$. So both functions behave like $x^{1/2}$ when $x \to \infty$ and $\lim \frac {f(x)} {g(x)}=\frac {\pi} 4$ as $x \to \infty$.

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  • $\begingroup$ I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $\pi/4$. $\endgroup$ – Toffomat Jan 16 at 9:30
  • $\begingroup$ @Toffomat Right. Thanks for pointing out. $\endgroup$ – Kavi Rama Murthy Jan 16 at 9:32

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