Question Number 170106 by Beginner last updated on 16/May/22
Answered by cortano1 last updated on 17/May/22
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{5}^{{x}} \:\mathrm{sin}\:\left(\frac{{a}}{\mathrm{5}^{{x}} }\right)\: \\ $$$$\:{let}\:\frac{\mathrm{1}}{\mathrm{5}^{{x}} }\:=\:{t}\: \\ $$$$\:=\:\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{at}}{{t}}\:=\:{a} \\ $$