# Comparing two infinitely large functions

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/

$$f(x)=x^{1/2} \frac {\arctan (x)} {\sqrt {4+\frac 3 x}}$$ 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 $$x \to \infty$$.
• I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $\pi/4$. – Toffomat Jan 16 at 9:30