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Author: Tinku Tara

lim-x-2-log-x-2-1-log-2-1-x-1-

Question Number 66478 by hmamarques1994@gmail.com last updated on 15/Aug/19 $$\: \\ $$$$\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\left[\frac{\boldsymbol{{log}}_{\boldsymbol{{x}}} \left(\mathrm{2}\right)−\mathrm{1}}{\boldsymbol{{log}}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)+\mathrm{1}}\right]=? \\ $$$$\: \\ $$ Commented by gunawan last updated on…

Question-66476

Question Number 66476 by aliesam last updated on 15/Aug/19 Commented by kaivan.ahmadi last updated on 15/Aug/19 $${t}=\mathrm{4}{x}+\mathrm{1}\Rightarrow \\ $$$$\frac{\left({t}−\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow\frac{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{t}}+\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow \\…

Question-132007

Question Number 132007 by abdullahquwatan last updated on 10/Feb/21 Answered by bramlexs22 last updated on 10/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}+\mathrm{sin}\:\mathrm{3x}\left(\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{2x}\right)−\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:\mathrm{2x}−\mathrm{1}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{3x}\right)}{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}}…