Question Number 128592 by BHOOPENDRA last updated on 09/Jan/21 $$\int\int\int_{{V}} \bigtriangledown×{F}\:{dV}\:{where}\:{F}=\left({x}+\mathrm{2}{y}\right)\hat {{i}}−\mathrm{3}{z}\hat {{j}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{x}\hat {{k}} \\ $$$${and}\:{V}\:{is}\:{the}\:{closed}\:{region}\:{in}\:{first}\:{octant} \\ $$$${by}\:{the}\:{plane}\:\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}=\mathrm{4} \\ $$$$ \\ $$ Answered…
Question Number 128593 by Eric002 last updated on 08/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mid\mathrm{3}{x}−\mathrm{1}\mid−\mid\mathrm{3}{x}+\mathrm{1}\mid}{{x}} \\ $$ Commented by MJS_new last updated on 08/Jan/21 $$\frac{\mid\mathrm{3}{x}−\mathrm{1}\mid−\mid\mathrm{3}{x}+\mathrm{1}\mid}{{x}}=\frac{\mathrm{3}}{{x}}\left(\mid{x}−\frac{\mathrm{1}}{\mathrm{3}}\mid−\mid{x}+\frac{\mathrm{1}}{\mathrm{3}}\mid\right)= \\ $$$$\:\:\:\:\:\left[−\frac{\mathrm{1}}{\mathrm{3}}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{3}}\right] \\ $$$$=\frac{\mathrm{3}}{{x}}\left(−\mathrm{2}{x}\right)=−\frac{\mathrm{6}{x}}{{x}}=−\mathrm{6}\forall{x}\in\left[−\frac{\mathrm{1}}{\mathrm{3}};\:\frac{\mathrm{1}}{\mathrm{3}}\right]\wedge{x}\neq\mathrm{0}…
Question Number 128590 by I want to learn more last updated on 08/Jan/21 Answered by mr W last updated on 08/Jan/21 Commented by mr W…
Question Number 128591 by BHOOPENDRA last updated on 09/Jan/21 $${verify}\:{the}\:{gauss}\:{divergence}\:{theorem} \\ $$$${f}=\left({x}^{\mathrm{2}} −{yz}\right)\hat {{i}}+\left({y}^{\mathrm{2}} −{zx}\right)\hat {\mathrm{j}}+\left({z}^{\mathrm{2}} −{xy}\right)\hat {{k}} \\ $$$${over}\:{the}\:{region}\:{R}\:{bounded}\:{by}\:{the}\: \\ $$$$ \\ $$$${parallelepiped}\:\mathrm{0}\leqslant{x}\leqslant{a},\mathrm{0}\leqslant{y}\leqslant{b}, \\…
Question Number 63054 by jimful last updated on 28/Jun/19 $${if}\:\Sigma\mid{a}_{{n}} \:\mid\:{is}\:{convergent},\:{then} \\ $$$${prove}\:{that}\:{there}\:{exists}\: \\ $$$${a}\:{subsequence}\:\left\{{n}_{{k}} {a}_{{n}_{{k}} } \right\}\:\:{with} \\ $$$$\underset{{k}\rightarrow\infty} {\mathrm{lim}}{n}_{{k}} {a}_{{n}_{{k}} } =\mathrm{0} \\…
Question Number 128589 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{a}\in\mathbb{R}^{+} \:\: \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\&\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\right\}\Rightarrow\:\sqrt{{a}−\sqrt{{a}}\:}\:=? \\ $$$$\:\:\:\:\:{a}^{\mathrm{2}} −\mathrm{17}{a}=\mathrm{16}\sqrt{{a}}\: \\ $$$$\:\:\:\:\:\:\: \\ $$ Answered by snipers237…
Question Number 128586 by ajfour last updated on 08/Jan/21 Commented by ajfour last updated on 08/Jan/21 $${Cubic}\:{curve}\:{eq}.\:\:{y}={x}^{\mathrm{3}} −{x}−{c} \\ $$$${Circle}\:{eq}.\:\:\:{x}^{\mathrm{2}} +\left({y}+{k}\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$ Terms…
Question Number 128582 by john_santu last updated on 08/Jan/21 $$\:\:\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)=? \\ $$ Answered by liberty last updated on 08/Jan/21 $$\:\mathrm{T}\:=\:\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}}…
Question Number 128579 by john_santu last updated on 08/Jan/21 $$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}}{\mathrm{xy}^{\mathrm{2}} +\mathrm{y}}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128574 by mohammad17 last updated on 08/Jan/21 $${Does}\:{the}\:{function}\:{f}\left({z}\right)=\frac{\mathrm{3}{z}^{\mathrm{4}} −\mathrm{2}{z}^{\mathrm{3}} +\mathrm{8}{z}^{\mathrm{2}} −\mathrm{2}{z}+\mathrm{5}}{{z}−{i}}\: \\ $$$$ \\ $$$${continuous}\:{at}\:{z}={i}\:? \\ $$ Answered by MJS_new last updated on…