(Solved): Find: a. \[ \begin{array}{l} \lim _{x \rightarrow \infty} x \ln x /\left(x^{2}+1\right)=\lim _{x \ ...

Find: a. \[ \begin{array}{l} \lim _{x \rightarrow \infty} x \ln x /\left(x^{2}+1\right)=\lim _{x \rightarrow \infty} \frac{\ln x+1}{2 x}=\lim _{x \rightarrow \infty} \frac{\frac{1}{x}}{2}=\lim _{x \rightarrow \infty} \frac{1}{2 x} \\ =\frac{1}{2} \cdot \lim _{x \rightarrow \infty} \frac{1}{x}=\frac{1}{2}=0=0 \end{array} \]