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Author: Tinku Tara

Question-211819

Question Number 211819 by Spillover last updated on 22/Sep/24 Answered by TonyCWX08 last updated on 22/Sep/24 $${i}. \\ $$$${Benzene}\:{can}\:{be}\:{prepared}\:{from}\:{Phenol}\:{through}\:{reduction}. \\ $$$${Vapour}\:{of}\:{Phenol}\:{passes}\:{over}\:{heated}\:{Zinc}\:{Dust}. \\ $$$${Zinc}\:{Dust}\:{will}\:{reduces}\:{them}\:{into}\:{Benzene} \\ $$$$…

Question-211873

Question Number 211873 by Spillover last updated on 22/Sep/24 Answered by IbtisamAdnan last updated on 23/Sep/24 $$\:\:\:\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{4}} \frac{\left(\boldsymbol{\mathrm{cos}\alpha}\right)^{\mathrm{x}} −\left(\mathrm{sin}\alpha\right)^{\mathrm{x}} −\mathrm{cos}\:\mathrm{2}\alpha}{\mathrm{x}−\mathrm{4}} \\ $$$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{4}} \:\frac{\left(\boldsymbol{\mathrm{cos}\alpha}\right)^{\mathrm{x}} .\:\mathrm{ln}\:\mathrm{cos}\alpha\:\:−\:\left(\mathrm{sin}\:\alpha\right)^{\mathrm{x}} .\mathrm{ln}\:\mathrm{sin}\alpha}{\mathrm{1}}\left[\mathrm{L}\:\mathrm{hospital}\:\mathrm{rule}\right]…

set-x-y-z-x-2-y-2-z-2-1-certificate-4-3-2-1-3-x-2y-2z-5-1-3-dv-8-3-

Question Number 211800 by MrGaster last updated on 21/Sep/24 $$ \\ $$$$\boldsymbol{{set}}\:\boldsymbol{\Omega}=\left\{\left(\boldsymbol{{x}},\boldsymbol{{y}},\boldsymbol{{z}}\right)\mid\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} \leq\mathrm{1}\right\}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{certificat}}\mathrm{e}: \\ $$$$\:\:\frac{\mathrm{4}\boldsymbol{\pi}}{\mathrm{3}}\sqrt[{\mathrm{3}}]{\mathrm{2}}\leq\int\underset{\boldsymbol{\Omega}} {\int}\int\sqrt[{\mathrm{3}}]{\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{y}}−\mathrm{2}\boldsymbol{{z}}+\mathrm{5}}\boldsymbol{{dv}}\leq\frac{\mathrm{8}\boldsymbol{\pi}}{\mathrm{3}} \\ $$$$ \\ $$$$ \\…

prove-lim-x-1-5-x-1-x-1-5-

Question Number 211812 by mokys last updated on 21/Sep/24 $${prove}\:\underset{{x}\rightarrow\infty} {{lim}}\:\left(\:\mathrm{1}\:+\:\frac{\mathrm{5}}{{x}}\:\right)^{\frac{\mathrm{1}}{{x}}} −\:\mathrm{1}\:=\:\mathrm{5}\: \\ $$ Commented by mr W last updated on 22/Sep/24 $${wrong}! \\ $$$${the}\:{result}\:{should}\:{be}\:\mathrm{0}.…

Question-211796

Question Number 211796 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\sqrt{\frac{\mathrm{cos}\:\left({x}−{a}\right)}{\mathrm{sin}\:\left({x}+{a}\right)}}{dx}= \\ $$$$=\int\sqrt{\frac{\mathrm{cos}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{sin}\:{a}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{cos}\:{a}\:\mathrm{sin}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\right] \\ $$$$=\int\sqrt{\frac{{t}\mathrm{sin}\:{a}\:+\mathrm{cos}\:{a}}{{t}\mathrm{cos}\:{a}\:+\mathrm{sin}\:{a}}}×\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}= \\…