Question Number 132972 by rexford last updated on 17/Feb/21 Answered by Ar Brandon last updated on 17/Feb/21 $$\begin{vmatrix}{\mathrm{i}}&{\mathrm{j}}&{\mathrm{k}}\\{\mathrm{1}}&{−\mathrm{2}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{1}}&{−\mathrm{2}}\end{vmatrix}=\mathrm{7i}+\mathrm{5j}+\mathrm{k} \\ $$ Commented by rexford last updated…
Question Number 1851 by 112358 last updated on 14/Oct/15 $${A}\:{plane}\:{has}\:{equation}\:{x}−{z}=\mathrm{4}\sqrt{\mathrm{3}}. \\ $$$${The}\:{line}\:{l}\:{has}\:{vector}\:{equation} \\ $$$$\boldsymbol{{r}}=\lambda\left[\left({cos}\theta+\sqrt{\mathrm{3}}\right)\boldsymbol{{i}}+\left(\sqrt{\mathrm{2}}{sin}\theta\right)\boldsymbol{{j}}+\left({cos}\theta−\sqrt{\mathrm{3}}\right)\boldsymbol{{k}}\right] \\ $$$${where}\:\lambda\:{is}\:{a}\:{scalar}\:{parameter}. \\ $$$${If}\:{l}\:{meets}\:{the}\:{plane}\:{at}\:{P},\:{show}\:{that}, \\ $$$${as}\:\theta\:{varies},\:{P}\:\:{describes}\:{a}\:{circle}.\: \\ $$ Answered by 123456…
Question Number 132920 by liberty last updated on 17/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{x}−\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}} \\ $$ Answered by bobhans last updated on 17/Feb/21 $$\:{L}'{H}\ddot {{o}pital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:{x}−\mathrm{2cos}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{cos}\:{x}}\:=…
Question Number 132856 by bramlexs22 last updated on 17/Feb/21 $$\mathrm{Given}\:\mathrm{vector}\:\overset{\rightarrow} {{a}}\:=\:\hat {\mathrm{i}}+\hat {\mathrm{j}}+\hat {\mathrm{k}}\:,\:\overset{\rightarrow} {\mathrm{c}}=\hat {\mathrm{j}}−\hat {\mathrm{k}}\:; \\ $$$$\:\overset{\rightarrow} {\mathrm{a}}\:×\:\overset{\rightarrow} {\mathrm{b}}\:=\:\overset{\rightarrow} {\mathrm{c}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{a}}.\overset{\rightarrow} {\mathrm{b}}\:=\:\mathrm{3}\:\mathrm{then}\:\mid\overset{\rightarrow} {\mathrm{b}}\mid\:=\:?…
Question Number 132853 by EDWIN88 last updated on 17/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{paraboloid}\: \\ $$$$\mathrm{z}\:=\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\mathrm{which}\:\mathrm{is}\:\mathrm{closest}\:\mathrm{to}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\left(\mathrm{3},−\mathrm{6},\mathrm{4}\:\right) \\ $$ Answered by MJS_new last updated on 17/Feb/21…
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Question Number 132650 by aupo14 last updated on 15/Feb/21 Commented by mr W last updated on 15/Feb/21 $${what}\:{do}\:{you}\:{mean}\:{with}\:\boldsymbol{{A\&B}}? \\ $$ Commented by aupo14 last updated…
Question Number 66971 by Cmr 237 last updated on 21/Aug/19 $$\int\frac{\mathrm{dx}}{\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\:}}=? \\ $$$$\boldsymbol{\mathrm{p}\mathfrak{l}}\mathrm{ease}\:\mathrm{help} \\ $$ Commented by MJS last updated on 21/Aug/19 $$\int\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}=…
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