$\displaystyle \begin{array}{{>{\displaystyle}l}} \lim _{x\rightarrow 1+}\frac{\sqrt{x+3} +10}{x^{2} +3x-4}\\ Ta\ có:\ \lim _{x\rightarrow 1+}\left(\sqrt{x+3} +10\right) =12 >0\\ \lim _{x\rightarrow 1+}\left( x^{2} +3x-4\right) =0\ và\ x^{2} +3x-4 >0\ \forall x\geqslant 1\\ Do\ đó\lim _{x\rightarrow 1+}\frac{\sqrt{x+3} +10}{x^{2} +3x-4} =+\infty \end{array}$
