Question Number 99972 by bobhans last updated on 24/Jun/20
Commented by bemath last updated on 24/Jun/20
$$\mathrm{b}\:=\:\mathrm{9}\:\Rightarrow\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{a}}{\mathrm{2}\sqrt{\mathrm{ax}+\mathrm{9}}}\:=\:\frac{\mathrm{1}}{\mathrm{3}};\:\frac{\mathrm{a}}{\mathrm{6}}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{a}\:=\:\mathrm{2}\:.\:\Rightarrow\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt{\mathrm{9x}−\mathrm{4}}−\sqrt{\mathrm{5}}}{\mathrm{x}−\mathrm{1}}\:=\:\frac{\mathrm{9}}{\mathrm{2}\sqrt{\mathrm{5}}} \\ $$$$ \\ $$