Prove that a nonlinear function of x is a linear function of x for small x values

Question

I have a function of $x$ defined as below $$f(x)=\sqrt{\frac{1}{N^2}\sum_{l=0,l\neq k}^{N-1}\frac{\sin^2(\pi(l-k+x))}{\sin^2(\frac{\pi}{N}(l-k+x))}+\left|\frac{1}{N}\sum_{l=0}^{N-1}\exp(j2\pi lx/N)-1\right|^2}$$

When I plot this function for small $x$ values ($x<0.2$) it is a linear function of $x$. How can I show this theoretically?

Thanks in advance