Question Number 143252 by bramlexs22 last updated on 12/Jun/21
$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}\:\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:=? \\ $$
Answered by Olaf_Thorendsen last updated on 12/Jun/21
$$\frac{\mathrm{8}{x}−\mathrm{6}{x}\mathrm{sin}{x}+\mathrm{sin2}{x}}{{x}^{\mathrm{5}} }\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{10}}{{x}^{\mathrm{4}} }\:\rightarrow+\infty \\ $$