Question Number 62067 by naka3546 last updated on 15/Jun/19 $$\underset{{x}\:\rightarrow\:−\mathrm{1}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{1}}{\left({x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:\:=\:\:? \\ $$ Commented by gunawan last updated on 15/Jun/19 $$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{3}{x}^{\mathrm{2}}…
Question Number 127572 by mathocean1 last updated on 30/Dec/20 $$\mid\mathrm{1}+{iz}_{\mathrm{0}} \mid=\mid\mathrm{1}−{iz}_{\mathrm{0}} \mid \\ $$$${show}\:{that}\:{z}_{\mathrm{0}} \in\mathbb{R} \\ $$ Answered by mathmax by abdo last updated on…
a-6-2-2-2-i-b-1-i-Determinate-possible-values-of-n-N-such-such-that-a-n-R-and-b-n-iR-pure-imaginary-
Question Number 127567 by mathocean1 last updated on 30/Dec/20 $${a}=\frac{\sqrt{\mathrm{6}}}{\mathrm{2}}+\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{i}\:;\:{b}=\mathrm{1}+{i}. \\ $$$${Determinate}\:{possible}\:{values} \\ $$$${of}\:{n}\:\in\:\mathbb{N}\:{such}\:{such}\:{that}\:{a}^{{n}} \:\in\:\mathbb{R}\:{and} \\ $$$${b}^{{n}} \:\in\:{i}\mathbb{R}\:\left({pure}\:{imaginary}\right). \\ $$$$ \\ $$$$ \\ $$$$ \\…
Question Number 127558 by mohammad17 last updated on 30/Dec/20 $${if}\:{Z}={cos}\theta+{isin}\theta\:{prove}\:{that}\: \\ $$$$ \\ $$$${Z}^{\mathrm{5}} −\frac{\mathrm{1}}{{Z}^{\mathrm{2}} }=\mathrm{2}{isin}\mathrm{5}\theta\: \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\ $$ Commented by mohammad17…
Question Number 127554 by mathdave last updated on 30/Dec/20 Commented by Dwaipayan Shikari last updated on 30/Dec/20 $${Q}\:\mathrm{127307} \\ $$ Terms of Service Privacy Policy…
Question Number 127553 by mathocean1 last updated on 30/Dec/20 $${f}\left({x}\right)=\sqrt{\frac{{x}^{\mathrm{3}} }{{x}−\mathrm{1}}} \\ $$$${calculate}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{−} } {{lim}f}\left({x}\right)\:;\:\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}f}\left({x}\right);\:\underset{{x}\rightarrow\mathrm{1}^{−} } {{lim}f}\left({x}\right); \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{+} } {{lim}f}\left({x}\right);\:\underset{{x}\rightarrow+\infty}…
Question Number 62010 by aliesam last updated on 13/Jun/19 $${if}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −\mathrm{2}{xyz}=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$ \\ $$$$\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:+\:\frac{{dy}}{\:\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }}\:+\:\frac{{dz}}{\:\sqrt{\mathrm{1}−{z}^{\mathrm{2}}…
Question Number 127540 by mathocean1 last updated on 30/Dec/20 $${m},\:{n},\:\in\:\mathbb{N}\:;\:{d}\:{is}\:{the}\:{greatest} \\ $$$${common}\:{divisor}\:{of}\:{m}\:{and}\:{n}.\: \\ $$$${we}\:{suppose}\:{m}={dm}'\:{and}\:{n}={dn}'\: \\ $$$${with}\:{m}'\:{and}\:{n}'\:\in\:\mathbb{N}. \\ $$$${show}\:{that}\:\exists\:{u},{v}\:\in\:\mathbb{Z}\:{such}\: \\ $$$${that}\:{mu}−{nv}={d} \\ $$ Terms of Service…
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Question Number 127537 by mohammad17 last updated on 30/Dec/20 $${if}\:{a}\:{group}\:{contains}\:{all}\:{of}\:{the}\:{points}\:{that}\: \\ $$$${you}\:{collect}\:{then}\:{its}\:{a}\:{closed}\:{group}\: \\ $$$$ \\ $$$${prove}\:{this}\:{in}\:{complex}\:{number}\:? \\ $$ Commented by mohammad17 last updated on 30/Dec/20…