Question Number 164783 by mkam last updated on 21/Jan/22
Answered by Mathspace last updated on 21/Jan/22
$$={lim}_{{x}\rightarrow\mathrm{3}} \frac{{f}\left({x}\right)−{f}\left(\mathrm{3}\right)}{{x}−\mathrm{3}}×\frac{{x}−\mathrm{3}}{\left({x}−\mathrm{3}\right)\left({x}+\mathrm{3}\right)} \\ $$$$={lim}_{{x}\rightarrow\mathrm{3}} \frac{{f}\left({x}\right)−{f}\left(\mathrm{3}\right)}{{x}−\mathrm{3}}×{lim}_{{x}\rightarrow\mathrm{3}} \frac{\mathrm{1}}{{x}+\mathrm{3}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}{f}^{'} \left(\mathrm{3}\right) \\ $$