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Question-162847

Question Number 162847 by mkam last updated on 01/Jan/22 Answered by abdullahhhhh last updated on 01/Jan/22 $$\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{want}}\:\boldsymbol{\mathrm{vaule}}\:\boldsymbol{\mathrm{of}}\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{x}}=\boldsymbol{\Pi}/\mathrm{4}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{what}} \\ $$$$ \\ $$ Commented by mkam last…

Question-97305

Question Number 97305 by eidmarie last updated on 07/Jun/20 Answered by MJS last updated on 07/Jun/20 $$\mathrm{crazy}\:\mathrm{question} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{is} \\ $$$$−\mathrm{6}+\frac{\mathrm{97}\sqrt{\mathrm{11}}}{\mathrm{55}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{11}}}{\mathrm{3}}\:+\frac{\mathrm{1}}{\mathrm{10}}\left(\mathrm{9ln}\:\mathrm{5}\:−\mathrm{28ln}\:\mathrm{2}\right) \\ $$$$\Rightarrow \\ $$$${a}=−\mathrm{6}+\frac{\mathrm{97}\sqrt{\mathrm{11}}}{\mathrm{55}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{11}}}{\mathrm{3}}…

Question-97307

Question Number 97307 by eidmarie last updated on 07/Jun/20 Commented by john santu last updated on 07/Jun/20 $$\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\left(\frac{\mathrm{ln}\left(\mathrm{5x}+\mathrm{n}\right)−\mathrm{ln}\left(\mathrm{n}\right)}{\mathrm{n}}\right)\:\mathrm{dx} \\ $$ Commented by bemath…

Question-162834

Question Number 162834 by mkam last updated on 01/Jan/22 Answered by abdullahhhhh last updated on 01/Jan/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{tan}}\mathrm{2}\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{tan}}\mathrm{2}\boldsymbol{\mathrm{x}}}\:/\boldsymbol{\mathrm{x}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}+\mathrm{2}}{\mathrm{1}−\mathrm{2}}=−\mathrm{3} \\ $$$$ \\ $$…

Question-162833

Question Number 162833 by mkam last updated on 01/Jan/22 Answered by abdullahhhhh last updated on 01/Jan/22 $$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}} \\ $$$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\left(\mathrm{1}+\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\right)\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}} \\ $$$$\left(\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{x}}+\boldsymbol{{y}}} \right)\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}=\boldsymbol{{e}}^{\boldsymbol{{x}}+\boldsymbol{{y}}} \\ $$$$\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}=\frac{\boldsymbol{{e}}^{\boldsymbol{{x}}+\boldsymbol{{y}}} }{\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{x}}+\boldsymbol{{y}}}…