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Question-130649

Question Number 130649 by muneer0o0 last updated on 27/Jan/21 Answered by MJS_new last updated on 27/Jan/21 $$\int\frac{{dx}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}}}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{2}}{x}−\mathrm{1}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\frac{\mathrm{3}}{\mathrm{4}}\:\rightarrow\:{dx}={dt}\right] \\ $$$$=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\frac{{dt}}{\:\sqrt{{t}^{\mathrm{2}} −\frac{\mathrm{25}}{\mathrm{16}}}}= \\…

y-sgn-x-y-

Question Number 130629 by Khalmohmmad last updated on 27/Jan/21 $${y}={sgn}\left({x}\right) \\ $$$$\acute {{y}}=? \\ $$ Answered by MJS_new last updated on 27/Jan/21 $$\mathrm{sgn}\:{x}\::=\begin{cases}{−\mathrm{1};\:{x}<\mathrm{0}}\\{\mathrm{0};\:{x}=\mathrm{0}\:^{\left(\mathrm{1}\right)} }\\{\mathrm{1};\:{x}>\mathrm{0}}\end{cases} \\…

solve-the-equation-sinz-i-

Question Number 130619 by mohammad17 last updated on 27/Jan/21 $${solve}\:{the}\:{equation}\:{sinz}={i}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 27/Jan/21 $$\frac{{e}^{{iz}} −{e}^{−{iz}} }{\mathrm{2}{i}}={i}\Rightarrow{e}^{\mathrm{2}{iz}} +\mathrm{2}{e}^{{iz}} −\mathrm{1}=\mathrm{0}\Rightarrow{e}^{{iz}}…

Question-130607

Question Number 130607 by Study last updated on 27/Jan/21 $$\infty^{\infty} =? \\ $$ Commented by MJS_new last updated on 27/Jan/21 $$\infty^{\infty} =?\:\left(\mathrm{1}\:\mathrm{question}\:\mathrm{mark}!\:\Rightarrow\:\mathrm{easy}!!\right) \\ $$$$\mathrm{0}^{\mathrm{0}} =??\:\left(\mathrm{2}\:\mathrm{question}\:\mathrm{marks}!!!\:\Rightarrow\:\mathrm{medium}!!!!\right)…

Question-65077

Question Number 65077 by naka3546 last updated on 24/Jul/19 Answered by MJS last updated on 25/Jul/19 $$\left(\mathrm{1}\right) \\ $$$${a}+{b}+\left({c}^{\mathrm{2}} −\mathrm{8}{c}+\mathrm{14}\right)\sqrt{{a}+{b}−\mathrm{2}}=\mathrm{1} \\ $$$$\sqrt{{a}+{b}−\mathrm{2}}={t}\Rightarrow{t}\geqslant\mathrm{0} \\ $$$$\Rightarrow\:{a}+{b}={t}^{\mathrm{2}} +\mathrm{2}…