The concept of generalised functions (distributions) and derivatives

Desvl at 
IntroductionTo begin with we consider a calculus problem that you may have seen in your exam:Let \(f\) be a continuous function on \([0,\infty)\) that \(\lim_{x \to \infty} f(x)=l\). Prove that \[\int_0^\infty \frac{f(ax)-f(bx)}{x}\mathrm{d}x = (f(0)-l)\ln\frac{b}{a}\]And we solve this problem as fo……