Question Number 177673 by DAVONG last updated on 08/Oct/22
$$\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{a}^{\mathrm{x}} −\mathrm{xlna}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{Help}\:\:\mathrm{please}\:\mathrm{Teacher} \\ $$
Commented by mr W last updated on 08/Oct/22
$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{ln}\:{a}\right){a}^{{x}} −\mathrm{ln}\:{a}}{\mathrm{2}{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{ln}\:{a}\right)^{\mathrm{2}} {a}^{{x}} }{\mathrm{2}} \\ $$$$=\frac{\left(\mathrm{ln}\:{a}\right)^{\mathrm{2}} }{\mathrm{2}} \\ $$