I have the following function; $$f(x) = -\frac{x}{2x + 4}\cdot v_r \Rightarrow \hat{f}(x) = -\frac{x}{4}\cdot v_r$$
Because $x$ is very small we can approximate $f(x)$ to $\hat{f}(x)$.
Now the relative error is computed. From my numerical methods course I know the relative error is defined as the real value minus the approximate value, the absolute error, divided by the real value. This is also stated on wikipedia;
$$ \eta_1 = \left|\frac{f(x) - \hat{f}(x)}{f(x)}\right|$$
However in the course I follow they say it is defined as;
$$ \eta_2 = \left|\frac{f(x) - \hat{f}(x)}{\hat{f}(x)}\right|$$
Now when I calculate $\eta_1$ and $\eta_2$ I get;
$$ \eta_1 = \left|\frac{x}{2}\right|$$
$$ \eta_2 = \left|\frac{x}{x + 2}\right|$$
Now my question is is that I don't really understand what the difference is between $\eta_1$ and $\eta_2$.
ps. if anyone can come up with a better topic title, or tags feel free.