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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}…

0-3-x-x-2-x-2-dx-

Question Number 64984 by naka3546 last updated on 23/Jul/19 $$\underset{\mathrm{0}} {\int}\:\overset{\mathrm{3}} {\:}\:{x}\:\mid{x}^{\mathrm{2}} \:−\:{x}\:−\:\mathrm{2}\mid\:{dx}\:\:=\:\:? \\ $$ Commented by kaivan.ahmadi last updated on 23/Jul/19 $${x}^{\mathrm{2}} −{x}−\mathrm{2}=\mathrm{0}\Rightarrow{x}=−\mathrm{1},\mathrm{2} \\…