Question Number 94769 by Hamida last updated on 20/May/20
Answered by i jagooll last updated on 21/May/20
Answered by mathmax by abdo last updated on 21/May/20
$$\mathrm{f}^{'} \left(\mathrm{5}\right)\:=\mathrm{lim}_{\mathrm{h}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{f}\left(\mathrm{5}+\mathrm{h}\right)−\mathrm{f}\left(\mathrm{5}\right)}{\mathrm{h}}\:=\mathrm{lim}_{\mathrm{h}\rightarrow\mathrm{0}} \:\:\:\frac{\frac{\mathrm{2}}{\mathrm{7}\left(\mathrm{5}+\mathrm{h}\right)−\mathrm{4}}−\frac{\mathrm{2}}{\mathrm{35}−\mathrm{4}}}{\mathrm{h}} \\ $$$$=\mathrm{lim}_{\mathrm{h}\rightarrow\mathrm{0}} \:\:\:\:\frac{\frac{\mathrm{2}}{\mathrm{31}+\mathrm{7h}}−\frac{\mathrm{2}}{\mathrm{31}}}{\mathrm{h}}\:=\mathrm{2lim}_{\mathrm{h}\rightarrow\mathrm{0}} \:\:\:\frac{−\mathrm{7h}}{\mathrm{31}\left(\mathrm{31}+\mathrm{7h}\right)\mathrm{h}} \\ $$$$=\mathrm{2}\:\mathrm{lim}_{\mathrm{h}\rightarrow\mathrm{0}} \:\:\:\:\frac{−\mathrm{7}}{\mathrm{31}\left(\mathrm{31}+\mathrm{7h}\right)}\:=\frac{−\mathrm{14}}{\mathrm{31}^{\mathrm{2}} }\:=−\frac{\mathrm{14}}{\mathrm{961}} \\ $$$$ \\ $$