Question Number 67561 by azizullah last updated on 28/Aug/19 Answered by Rasheed.Sindhi last updated on 28/Aug/19 $${Let}\:\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{1}\right)}=\frac{{Ax}+{B}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{{C}}{{x}−\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\left({Ax}+{B}\right)\left({x}−\mathrm{1}\right)+{C}\left({x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{2}{x}+\mathrm{1} \\ $$$${x}=\mathrm{1}\Rightarrow\mathrm{2}{C}=\mathrm{3}\Rightarrow{C}=\mathrm{3}/\mathrm{2} \\…
Question Number 133094 by mohammad17 last updated on 18/Feb/21 Commented by mohammad17 last updated on 18/Feb/21 $${how}\:{can}\:{prove}\:{this} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 133075 by LUFFY last updated on 18/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} +{k}^{\mathrm{2}} }\right)\:{k}\in?????? \\ $$ Answered by Dwaipayan Shikari last updated on 18/Feb/21 $$\frac{\mathrm{1}}{\mathrm{2}{ik}}\underset{{n}=\mathrm{1}}…
Question Number 67516 by LPM last updated on 28/Aug/19 Commented by Prithwish sen last updated on 28/Aug/19 $$\mathrm{cos}^{\mathrm{2}} \mathrm{x}\:+\left(\mathrm{2cos}^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} =\:\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \mathrm{3x} \\ $$$$\mathrm{Simplyfying}\:\mathrm{we}\:\mathrm{get}, \\…
Question Number 133028 by mohammad17 last updated on 18/Feb/21 Answered by Dwaipayan Shikari last updated on 18/Feb/21 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{1},\mathrm{1}\right)} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}−{y}}={x}+{y}=\mathrm{2} \\ $$ Terms of…
Question Number 133010 by rs4089 last updated on 18/Feb/21 $${for}\:{the}\:{extremum}\:{values}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:{subject}\:{to}\:{the}\:{constraints} \\ $$$${ax}^{\mathrm{2}} +{by}^{\mathrm{2}} +{cz}^{\mathrm{2}} =\mathrm{1}\:{and}\:{lx}+{my}+{nz}=\mathrm{0}\:. \\ $$$${show}\:{that}\:{the}\:{stationary}\:{points}\:{setisfy}\:{the}\:{realation} \\ $$$$\frac{{l}^{\mathrm{2}} }{\mathrm{1}+{a}\lambda_{\mathrm{1}} }+\frac{{m}^{\mathrm{2}} }{\mathrm{1}+{b}\lambda_{\mathrm{1}}…
Question Number 132991 by aurpeyz last updated on 17/Feb/21 $${A}\:{convex}\:{lens}\:{of}\:{focal}\:{length}\:\mathrm{10}{cm} \\ $$$${is}\:{used}\:{to}\:{form}\:{a}\:{real}\:{image}\:{which}\:{is} \\ $$$${half}\:{the}\:{size}\:{of}\:{the}\:{object}.\:{how}\:{far} \\ $$$${from}\:{the}\:{object}\:{is}\:{the}\:{image}??? \\ $$ Commented by aurpeyz last updated on 17/Feb/21…
Question Number 132967 by mohammad17 last updated on 17/Feb/21 $${where}\:{is}\:{function}\:{f}\left({z}\right)={zRez}+\overset{−} {{z}lnz}+\overset{−} {{z}} \\ $$$${derivable}\:,{then}\:{find}\:{the}\:{dervaitive}\:? \\ $$ Commented by mohammad17 last updated on 18/Feb/21 $$????\:\: \\…
Question Number 67431 by aliesam last updated on 27/Aug/19 Commented by mathmax by abdo last updated on 27/Aug/19 $${if}\:{a}\:{and}\:{b}\:{from}\:{C}\:{the}\:{question}\:{is}\:{done}\:{by}\:{sir}\:{mjs} \\ $$$${if}\:{a}\:{and}\:{b}\:{from}\:{R}\:\:\:{we}\:{have}\:\:\left(\mid\frac{{a}}{{b}}\mid\right)^{\mathrm{2}} −\left(\frac{\mid{a}\mid}{\mid{b}\mid}\right)^{\mathrm{2}} \: \\ $$$$=\mid\frac{{a}^{\mathrm{2}}…
Question Number 132954 by LUFFY last updated on 17/Feb/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left({x}\right)−{cos}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 17/Feb/21 $${I}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty}…