$f(x) = \sqrt{x^{2}+1}-1$ (Loss of Significance)
Assume that due to rounding errors, when you try to calculate the square root of $x^2 + 1$ you actually get the square root plus $\epsilon$ for some small $\epsilon$. Assume that $\epsilon = 10^{-10}$ and $x = 10^{-6}$. Perform the calculations and write down the results.