Question Number 155642 by mathlove last updated on 03/Oct/21
Commented by cortano last updated on 03/Oct/21
$$\mathrm{8}\sqrt{\mathrm{2}}\:\mathrm{ln}\:^{\mathrm{2}} \left(\mathrm{3}\right) \\ $$
Commented by mathlove last updated on 03/Oct/21
$${solution} \\ $$
Commented by cortano last updated on 03/Oct/21
$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{3}^{\mathrm{x}} −\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{x}}\right)^{\mathrm{2}} = \\ $$$$\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}×\left(\mathrm{ln}\:\mathrm{3}\right)^{\mathrm{2}} ×\mathrm{16} \\ $$