Question Number 4772 by Yozzii last updated on 07/Mar/16 $${Let}\:{z}={Ax}^{\mathrm{2}} +{Bxy}+{Cy}^{\mathrm{2}} .\:{Find}\:{conditions} \\ $$$${on}\:{the}\:{constants}\:{A},{B},{C}\:{that}\:{ensure} \\ $$$${that}\:{the}\:{point}\:\left(\mathrm{0},\mathrm{0},\mathrm{0}\right)\:{is}\:{a}\: \\ $$$$\left({i}\right)\:{local}\:{minimum}, \\ $$$$\left({ii}\right)\:{local}\:{maximum}, \\ $$$$\left({ii}\right)\:{saddle}\:{point}. \\ $$$$ \\…
Question Number 4596 by Yozzii last updated on 10/Feb/16 $${Use}\:{the}\:{definition}\:{of}\:{the}\:{limit}\:{of}\:{a}\:{function} \\ $$$${to}\:{prove}\:{that}\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\frac{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }=\mathrm{0}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 135630 by rexford last updated on 14/Mar/21 Answered by mr W last updated on 14/Mar/21 Commented by mr W last updated on 14/Mar/21…
Question Number 135054 by rexford last updated on 09/Mar/21 Commented by mr W last updated on 10/Mar/21 $${there}\:{are}\:{three}\:{possible}\:{answers}: \\ $$$${in}\:{plane}:\:\mid{a}\mid=\frac{\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$$${in}\:{space}:\:\mid{a}\mid=\mathrm{1}\:{or}\:\sqrt{\mathrm{3}} \\ $$ Commented…
Question Number 134949 by rexford last updated on 08/Mar/21 Answered by bobhans last updated on 30/Jan/22 $$\overset{\rightarrow} {\mathrm{b}}\:=\:\mathrm{2}\overset{\rightarrow} {\mathrm{c}}+\lambda\overset{\rightarrow} {\mathrm{a}}\:;\:\mid\overset{\rightarrow} {\mathrm{b}}\mid\:=\:\mid\mathrm{2}\overset{\rightarrow} {\mathrm{c}}+\lambda\overset{\rightarrow} {\mathrm{a}}\mid \\ $$$$\Rightarrow\:\mathrm{4}\:=\:\sqrt{\mid\mathrm{2}\overset{\rightarrow}…
Question Number 68836 by Joel122 last updated on 16/Sep/19 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of} \\ $$$$\boldsymbol{{r}}\:=\:\left(\mathrm{sin}\:{t}\right)\boldsymbol{{i}}\:+\:\left(\mathrm{2cos}\:{t}\right)\boldsymbol{{j}}\:+\:\left(\sqrt{\mathrm{3}}\mathrm{sin}\:{t}\right)\boldsymbol{{k}} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{circle} \\ $$ Answered by Tanmay chaudhury last updated on 16/Sep/19 $${ix}+{jy}+{kz}=\left({sint}\right){i}+\left(\mathrm{2}{cost}\right){j}+\left(\sqrt{\mathrm{3}}\:{sint}\right){k}…
Question Number 133937 by rexford last updated on 25/Feb/21 Answered by EDWIN88 last updated on 25/Feb/21 $$\boldsymbol{{AB}}\:=\:\hat {\boldsymbol{\mathrm{i}}}+\mathrm{6}\hat {\boldsymbol{\mathrm{j}}}\:,\:\mathrm{let}\:\mathrm{vector}\:\boldsymbol{\mathrm{u}}\:=\:\boldsymbol{\mathrm{AC}}\:\mathrm{where}\:\mathrm{C}\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\boldsymbol{\mathrm{u}}=\left(\mathrm{x}−\mathrm{1},\mathrm{y}+\mathrm{1}\right)\:=\left(\mathrm{x}−\mathrm{1}\right)\hat {\boldsymbol{\mathrm{i}}}+\left(\mathrm{y}+\mathrm{1}\right)\hat {\boldsymbol{\mathrm{j}}} \\ $$$$\Rightarrow\:\boldsymbol{\mathrm{u}}.\boldsymbol{\mathrm{AB}}\:=\mathrm{0}\:\Rightarrow\mathrm{x}−\mathrm{1}+\mathrm{6y}+\mathrm{6}\:=\:\mathrm{0}…
Question Number 133445 by benjo_mathlover last updated on 22/Feb/21 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{2x}−\mathrm{2y}+\mathrm{z}+\mathrm{12}=\mathrm{0} \\ $$$$\mathrm{touches}\:\mathrm{the}\:\mathrm{sphere}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} −\mathrm{2x}−\mathrm{4y}+\mathrm{2z}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{contact}\:. \\ $$ Answered by MJS_new last updated on…
Question Number 133392 by rexford last updated on 21/Feb/21 Commented by EDWIN88 last updated on 22/Feb/21 $$\mathrm{qn}\:\mathrm{133398} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 133398 by rexford last updated on 21/Feb/21 Answered by EDWIN88 last updated on 22/Feb/21 $$\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{b}}+\overset{\rightarrow} {{b}}.\overset{\rightarrow} {{c}}=\left(\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{c}}\right).\overset{\rightarrow} {{b}}=−\overset{\rightarrow} {{b}}.\overset{\rightarrow}…