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Author: Tinku Tara

Question-204397

Question Number 204397 by Abdullahrussell last updated on 16/Feb/24 Answered by MM42 last updated on 16/Feb/24 $$\left({y}−\mathrm{1}\right)\left({y}+\mathrm{1}\right)\left({y}^{\mathrm{2}} +\mathrm{1}\right)={x}\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$\Rightarrow{y}={x}\Rightarrow\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}+\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}={y}=−\mathrm{1}\:\checkmark \\…

Question-204396

Question Number 204396 by Thierrybadouana last updated on 15/Feb/24 Answered by Faetmaaa last updated on 27/Feb/24 $$\mathrm{ln}\left(\mathrm{1}+{y}\right)\:\underset{{y}\rightarrow\mathrm{0}} {\sim}\:{y} \\ $$$$\mathrm{sin}\left({y}\right)\:\underset{{y}\rightarrow\mathrm{0}} {\sim}\:{y} \\ $$$$\underset{\begin{matrix}{{x}\rightarrow\mathrm{0}}\\{{x}\neq\mathrm{0}}\end{matrix}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{sin}^{\mathrm{2}}…