Let \( f:(0, \infty) \rightarrow R, f(x)=f(x)=\left(\frac{x+1}{x}\right)^{\left(\frac{x+1}{2}\ri...
Let \( f:(0, \infty) \rightarrow R, f(x)=f(x)=\left(\frac{x+1}{x}\right)^{\left(\frac{x+1}{2}\right)} \) and \( g(x)=\frac{f^{\prime}(x)}{f(x)} \), then then
(a) \( \mathrm{g}(\mathrm{x}) \) is increasing in \( (0, \infty) \)
(b) \( \lim _{x \rightarrow \infty} g(x)=0 \)
(c) \( \lim _{x \rightarrow \infty} f(x)=\sqrt{e} \)
(d) \( \lim _{x \rightarrow \infty} g(x)=\sqrt{e} \)
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