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lim-x-2-7-log-x-256-1-3-49-2-2-x-1-4-

Question Number 67958 by hmamarques1994@gmai.com last updated on 02/Sep/19 $$\: \\ $$$$\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}} {\boldsymbol{\mathrm{lim}}}\left(\frac{\mathrm{7}^{\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{log}}_{\boldsymbol{\mathrm{x}}} \left(\mathrm{256}\right)}} −\mathrm{49}}{\mathrm{2}^{−\sqrt{\mathrm{2}^{\boldsymbol{\mathrm{x}}} }} −\frac{\mathrm{1}}{\mathrm{4}}}\right)\:\approx\:? \\ $$$$\: \\ $$ Terms of Service Privacy…

Question-67918

Question Number 67918 by aliesam last updated on 02/Sep/19 Answered by $@ty@m123 last updated on 02/Sep/19 $${Let}\:\alpha+\beta={x} \\ $$$$\mathrm{tan}\:{x}=\frac{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}}=\mathrm{1}\Rightarrow{x}=\mathrm{45}^{\mathrm{o}} \:\:…\left(\mathrm{1}\right) \\ $$$$\mathrm{tan}\:\beta=\frac{\mathrm{1}}{\mathrm{3}}\Rightarrow\mathrm{sin}\:\beta=\frac{\mathrm{1}}{\:\sqrt{\mathrm{10}}}\:\&\:\mathrm{cos}\:\beta=\frac{\mathrm{3}}{\:\sqrt{\mathrm{10}}}\:..\left(\mathrm{2}\right) \\ $$$$\therefore\:\mathrm{cos}\:\left(\mathrm{12}\alpha+\mathrm{13}\beta\right)=\mathrm{cos}\:\left(\mathrm{12}{x}+\beta\right) \\…