Solution
= Solution
The central <limit> theorem and Delta method give
$$
\sqrt n\{g(\bar X_n)-g(\mu)\}
\Rightarrow N(0,g'(\mu)^2\sigma^2).
$$
Thus one may take
$$
\boxed{\sigma_n=\frac{|g'(\mu)|\sigma}{\sqrt n}.}
$$
= Solution
The central <limit> theorem and Delta method give
$$
\sqrt n\{g(\bar X_n)-g(\mu)\}
\Rightarrow N(0,g'(\mu)^2\sigma^2).
$$
Thus one may take
$$
\boxed{\sigma_n=\frac{|g'(\mu)|\sigma}{\sqrt n}.}
$$