If I have a function $$f(x)=\frac{a}{a+ax+(1-a)\sqrt{x}}$$ where $0\le a \le1$, $x>0$. Then, what's the dominant term in denominator when $x\to 0$?
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1$\lim_{x \to 0} f(x)=1$. – Dec 20 '17 at 11:33
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@Rohan What happens if $a=0$? – Michael Rozenberg Dec 20 '17 at 11:35
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In case it's not clear: Aside from the particular case when $a=0$, Rohan's comment gives the correct dominant term of $f(x)$. The dominant term in the denominator is clearly $a$ when $a > 0$ because everything else goes to $0$. – Antonio Vargas Dec 20 '17 at 17:27