Menu Close

Question-176692




Question Number 176692 by mnjuly1970 last updated on 25/Sep/22
Commented by cortano1 last updated on 25/Sep/22
 Ω = 8π^4
$$\:\Omega\:=\:\mathrm{8}\pi^{\mathrm{4}} \\ $$
Answered by blackmamba last updated on 25/Sep/22
  Ω=lim_(x→0)  ((sin^4 (π cos x))/(1−cos (1−cos (((sin^2 x)/2)))))   Ω= lim_(x→0)  ((sin^4 (π cos x))/(1−cos (((sin^2 (((sin^2 x)/2)))/2))))  Ω= lim_(x→0)  ((sin^4 (π cos x))/((sin^2 (((sin^2 (((sin^2 x)/2)))/2)))/2)) = ∞
$$\:\:\Omega=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} \left(\pi\:\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{2}}\right)\right)} \\ $$$$\:\Omega=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} \left(\pi\:\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{2}}\right)}{\mathrm{2}}\right)} \\ $$$$\Omega=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} \left(\pi\:\mathrm{cos}\:{x}\right)}{\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{2}}\right)}{\mathrm{2}}\right)}{\mathrm{2}}}\:=\:\infty \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *