Question Number 194256 by horsebrand11 last updated on 01/Jul/23
$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}{\mathrm{1}−\mathrm{tan}\:\mathrm{x}}\:−\mathrm{1}}{\mathrm{x}}\:=? \\ $$
Answered by tri26112004 last updated on 01/Jul/23
$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{tan}\:{x}}{{x}\left(\mathrm{1}−{tan}\:{x}\right)} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{tan}\:{x}}{{x}}\:.\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}}{\mathrm{1}−{tan}\:{x}} \\ $$$$=\:\mathrm{1}\:.\:\frac{\mathrm{2}}{\mathrm{1}−\mathrm{0}}\:=\:\mathrm{2} \\ $$
Answered by cortano12 last updated on 01/Jul/23
$$\:\:\:\cancel{\lesseqgtr} \\ $$