List of top Mathematics Questions on Limits asked in AP EAMCET

Let \(f:\mathbb{R}^+\to\mathbb{R}^+\) be a function satisfying
\[ f(x)-x=\lambda \text{ constant},\quad \forall x\in\mathbb{R}^+ \] and
\[ f(f(y))=f(xy)+x,\quad \forall x,y\in\mathbb{R}^+. \] Then
\[ \lim_{x\to0}\frac{(f(x))^{1/3}-1}{(f(x))^{1/2}-1}= \]

If
\[ \lim_{x\to0}\frac{|x|}{\sqrt{x^4+4x^2+5}}=k, \] and
\[ \lim_{x\to0}x^4\sin\left(\frac{1}{3\sqrt{x}}\right)=l, \] then \(k+l=\)

If
\[ \lim_{x\to\infty}x^{\log_e x}=0, \] then \(\log_x12=\)