Question Number 5165 by 1771727373 last updated on 24/Apr/16 $${what}\:{is} \\ $$$$\sqrt{{i}+\mathrm{1}}\:\:\:\:? \\ $$ Commented by FilupSmith last updated on 24/Apr/16 $$\mathrm{assuming}\:{i}^{\mathrm{2}} =−\mathrm{1}, \\ $$$$\mathrm{according}\:\mathrm{to}\:\mathrm{WolframAlpha}:…
Question Number 70696 by Erik_Regiomontan last updated on 07/Oct/19 $$\int{x}^{{x}} {dx}=? \\ $$ Commented by sadimuhmud 136 last updated on 07/Oct/19 $$\mathrm{error}\:\mathrm{question}.. \\ $$$$ \\…
Question Number 70694 by oyemi kemewari last updated on 07/Oct/19 Answered by mind is power last updated on 07/Oct/19 $${let}\:\frac{{y}'}{{x}}={u} \\ $$$$\Rightarrow{y}'={xu}\Rightarrow{y}''={u}+{xu}' \\ $$$${xy}''={xu}+{x}^{\mathrm{2}} {u}'…
Question Number 5159 by 1771727373 last updated on 24/Apr/16 $${a}+\mathrm{24}\frac{{a}−\mathrm{3}}{{b}^{\mathrm{2}} +{a}}=\mathrm{2}{a}−{b}^{\mathrm{2}\:} \\ $$$${a}×{b}^{\mathrm{2}} =\mathrm{20} \\ $$$$ \\ $$$${would}\:{you}\:{solve}\:{this}? \\ $$ Answered by FilupSmith last updated…
Question Number 5158 by 1771727373 last updated on 24/Apr/16 $${why} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:+\:………..\:=\:\mathrm{2} \\ $$$$ \\ $$ Answered by FilupSmith last updated on 24/Apr/16 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+…={S} \\…
Question Number 5157 by 1771727373 last updated on 24/Apr/16 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+……..={S} \\ $$$$\mathrm{2}+\mathrm{4}+\mathrm{6}+\mathrm{8}+\mathrm{10}+……..=\mathrm{2}{S} \\ $$$${S}\supset\mathrm{2}{S} \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+…………+\left(\mathrm{2}{S}\right)={S} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left\{\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}}\right\}=+\infty \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left\{{n}^{\mathrm{2}} \right\}=+\infty \\ $$$$\left(+\infty\right)+\left(+\infty\right)={S}=\infty…
Question Number 136225 by mnjuly1970 last updated on 19/Mar/21 $$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:\:{calculus}\:\: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:{find}\:::\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {xe}^{−{x}} {coth}\left(\frac{{x}}{\mathrm{2}}\right){dx}=? \\ $$$$ \\ $$$$ \\ $$$$…
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Question Number 5153 by 1771727373 last updated on 23/Apr/16 $${proof}\:\:\:\:{e}^{{i}\Theta} ={cos}\left(\Theta\right)+{isin}\left(\Theta\right) \\ $$ Answered by 123456 last updated on 23/Apr/16 $$\mathrm{lets}\:{f}\left(\theta\right)=\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta,{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\frac{\partial{f}}{\partial\theta}=−\mathrm{sin}\:\theta+{i}\mathrm{cos}\:\theta={i}\left(\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta\right)={if} \\ $$$$\frac{{df}}{{f}}={id}\theta…
Question Number 5152 by 1771727373 last updated on 23/Apr/16 $${there}\:{is}\:{an}\:{ineterger}\:{a},{b},{c} \\ $$$${can}\:{there}\:{be}\:{an}\:{interger}\:{as}\: \\ $$$${a}^{{n}} +{b}^{{n}+\mathrm{1}} ={c}^{{n}+\mathrm{2}} \:\:\:\:\:\:\left({n}\:{is}\:{a}\:{interger}\right) \\ $$$$ \\ $$ Commented by Yozzii last…