Question Number 31676 by gunawan last updated on 12/Mar/18
![Given function f diferensiabel on R. If lim_(x→0) f((a/x)+b) non zero lim_(x→0) [f((a/x)+b)−(a/x)f′((a/x)+b)]=a how many value lim_(x→∞) f(x)](Q31676.png)
$$\mathrm{Given}\:\mathrm{function}\:{f}\:\mathrm{diferensiabel}\:\mathrm{on}\:\boldsymbol{\mathrm{R}}. \\ $$$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left(\frac{{a}}{{x}}+{b}\right)\:\mathrm{non}\:\mathrm{zero} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[{f}\left(\frac{{a}}{{x}}+{b}\right)−\frac{{a}}{{x}}{f}'\left(\frac{{a}}{{x}}+{b}\right)\right]={a} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{value}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$