Question Number 188699 by cortano12 last updated on 05/Mar/23
$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\right)=? \\ $$
Answered by mehdee42 last updated on 05/Mar/23
$${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{\mathrm{1}−{sinx}}{{cos}^{\mathrm{2}} {x}}\right)={li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{\mathrm{1}}{\mathrm{1}+{sinx}}\right)={A} \\ $$$${if}\:\:{x}=\mathrm{2}{n}\pi\:\Rightarrow{A}=\mathrm{1}\:\&\:{if}\:\:{x}=\mathrm{2}{n}\pi+\frac{\pi}{\mathrm{2}}\Rightarrow{A}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${therefore}\:\:,\:{there}\:\:{is}\:\:{no}\:{limit} \\ $$$$ \\ $$