Question Number 176394 by Matica last updated on 18/Sep/22
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−{cos}\sqrt{\mid{x}\mid}\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{{cosx}}}\:=\:? \\ $$
Commented by cortano1 last updated on 18/Sep/22
$$\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\mathrm{cos}\:\sqrt{\mid\mathrm{x}\mid}\:\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{\mathrm{cos}\:\mathrm{x}}}\:\left(\mathrm{DNE}\right) \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\mathrm{cos}\:\sqrt{\mid\mathrm{x}\mid}\:\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{\mathrm{cos}\:\mathrm{x}}}\:=\:\mathrm{4} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\mathrm{cos}\:\sqrt{\mid\mathrm{x}\mid}\:\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{\mathrm{cos}\:\mathrm{x}}}\:\left(\mathrm{DNE}\right) \\ $$