Question Number 76572 by john santu last updated on 28/Dec/19 $${how}\:{do}\:{you}\:{find}\:{the}\:{least}\:{value}\:{of}\:{x}^{\mathrm{2}} \\ $$$$+\mathrm{2}{xy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}{y}\:{using}\:{the}\: \\ $$$${concepts}\:{of}\:{algebra}\:{or}\:{calculus}?\: \\ $$ Answered by benjo 1/2 santuyy last updated…
Question Number 11036 by suci last updated on 08/Mar/17 $${l}\underset{{n}\rightarrow\sim} {{i}m}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{8}{n}^{\mathrm{2}} }{{n}^{\mathrm{4}} +\mathrm{1}}\:=….? \\ $$ Commented by FilupS last updated on 08/Mar/17 $${S}=\underset{{n}\rightarrow\infty}…
Question Number 142105 by PRITHWISH SEN 2 last updated on 26/May/21 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms} \\ $$$$\mathrm{sin}\:\theta−\mathrm{sin}\:\mathrm{2}\theta+\mathrm{sin}\:\mathrm{3}\theta−…….. \\ $$ Answered by Dwaipayan Shikari last updated on 26/May/21 $$\underset{{n}=\mathrm{1}}…
Question Number 11035 by suci last updated on 08/Mar/17 $${A}=\begin{bmatrix}{\mathrm{1}}&{−\mathrm{1}}\\{−\mathrm{4}}&{−\mathrm{2}}\end{bmatrix} \\ $$$${A}^{\mathrm{2016}} =…..? \\ $$ Answered by diofanto last updated on 19/Jul/17 $$\mathrm{Finding}\:\mathrm{the}\:\mathrm{eigenvalues}\:\mathrm{of}\:{A}: \\ $$$$\begin{vmatrix}{\mathrm{1}−\lambda}&{−\mathrm{1}}\\{−\mathrm{4}}&{−\mathrm{2}−\lambda}\end{vmatrix}\:=\:\mathrm{0}…
Question Number 11034 by suci last updated on 08/Mar/17 $${u}=\begin{bmatrix}{\mathrm{1}}&{−\mathrm{1}}&{\mathrm{2}}\end{bmatrix} \\ $$$${A}=\begin{bmatrix}{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{1}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{1}}\end{bmatrix} \\ $$$${v}=\begin{bmatrix}{\mathrm{2}}&{−\mathrm{1}}\end{bmatrix} \\ $$$${uAv}^{{t}} =….? \\ $$ Commented by bahmanfeshki last updated on…
Question Number 142100 by ZiYangLee last updated on 26/May/21 $$\:\:\:\:\:\:\int^{\:} \:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{1}+{t}}\:}\:{dt}=? \\ $$ Answered by iloveisrael last updated on 26/May/21 $${I}=\int\:\frac{{dt}}{\mathrm{1}+\sqrt{\mathrm{1}+{t}}}\:=\:\int\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{t}}}{−{t}}\:{dt} \\ $$$${I}=\int\:\frac{\sqrt{\mathrm{1}+{t}}}{{t}}\:{dt}\:−\mathrm{ln}\:{t}\:+{c} \\ $$$${let}\:\sqrt{\mathrm{1}+{t}}\:=\:{u}\Rightarrow{t}={u}^{\mathrm{2}}…
Question Number 142103 by rs4089 last updated on 26/May/21 $$\int_{−\infty} ^{\infty} \frac{{tan}^{−\mathrm{1}} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 142096 by mohammad17 last updated on 26/May/21 Commented by mohammad17 last updated on 26/May/21 $${help}\:{me}\:{sir}\:{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 11024 by ABD last updated on 07/Mar/17 $${P}\left({x}+\mathrm{1}\right)×{P}\left({x}−\mathrm{1}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{8}{x}+{a}−\mathrm{5} \\ $$$${a}=? \\ $$ Answered by ajfour last updated on 07/Mar/17 $${let}\:{P}\left({x}\right)\:=\:{bx}+{c} \\ $$$${Then}\:{P}\left({x}+\mathrm{1}\right)×{P}\left({x}−\mathrm{1}\right)…
Question Number 11023 by ABD last updated on 07/Mar/17 $$\left({x}^{\mathrm{3}} +\mathrm{6}\right)×{P}\left({x}\right)+\mathrm{6}{x}={ax}^{\mathrm{3}} +\mathrm{2}{ax}+{b}+\mathrm{3} \\ $$$$\Rightarrow{b}=? \\ $$ Answered by mrW1 last updated on 07/Mar/17 $$\left({x}^{\mathrm{3}} +\mathrm{6}\right)×{P}\left({x}\right)+\mathrm{6}{x}={ax}^{\mathrm{3}}…