Since I suspect that both cases have a similar apoach I combine these two.

According to exercise-exams of my university $\displaystyle \sqrt{1+(1/x^2)}$ is aproximately equal to $\displaystyle 1 + (1/2x^2)$ and $\displaystyle log{(1 + (1/4x^2))}$ aproximately equal to $\displaystyle 1/(4x^2)$

Why?