(Solved): Find the limit; use proper notation in your work. \[ \lim _{x \rightarrow 1}\left(\frac{1}{\ln (x)} ...

Find the limit; use proper notation in your work. \[ \lim _{x \rightarrow 1}\left(\frac{1}{\ln (x)}-\frac{x}{x-1}\right) \] Let \( \mathrm{a} \) and \( \mathrm{b} \) be positive real numbers. Find the limit. Write your answer in terms of \( \mathrm{a} \) and \( \mathrm{b} \). \[ \lim _{x \rightarrow \infty}\left(1+\frac{a}{x}\right)^{b x} \]