Question Number 195231 by cortano12 last updated on 28/Jul/23
$$\:\:\:\:\:\begin{array}{|c|}{\:\cancel{\underline{\underbrace{ }}}}\\\hline\end{array} \\ $$
Answered by MM42 last updated on 28/Jul/23
$${lim}_{{x}\rightarrow\mathrm{0}} \:\:\sqrt{\frac{\mathrm{1}−{cos}\sqrt{\pi{x}}}{{x}\left(\mathrm{1}+\sqrt{{cos}\sqrt{\pi{x}}}\right)}}\:\: \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}} \:\sqrt{\frac{\frac{\mathrm{1}}{\mathrm{2}}\pi{x}}{{x}\left(\mathrm{1}+\sqrt{\left.{cos}\sqrt{\pi{x}}\right)}\right.}} \\ $$$$=\sqrt{\frac{\pi}{\mathrm{4}}}\:=\frac{\sqrt{\pi}}{\mathrm{2}}\:\:\:\checkmark \\ $$
Commented by cortano12 last updated on 28/Jul/23
$${wrong} \\ $$
Commented by Frix last updated on 28/Jul/23
$$\mathrm{I}\:\mathrm{also}\:\mathrm{get}\:\frac{\sqrt{\pi}}{\mathrm{2}} \\ $$
Commented by mokys last updated on 29/Jul/23
$$\frac{\pi}{\mathrm{2}} \\ $$