考研真题

求极限 ${\lim }_{n\to \infty }\left(\frac{1}{\sqrt{n^2+1^2}}+\frac{1}{\sqrt{n^2+2^2}}+\cdots +\frac{1}{\sqrt{n^2+n^2}}\right).$

求极限 ${\lim }_{x\to +\infty }\left[x-x^3\ln \left(1+\frac{1}{x^2}\right)\right].$

求极限 ${\lim }_{x\to +\infty }\frac{\ln \sqrt{x}+{\sin }^{2}x}{x}.$