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Author: Tinku Tara

lets-f-R-Z-suppose-that-x-R-and-y-R-with-x-y-such-f-x-f-y-can-f-x-be-conrinuous-

Question Number 1196 by 123456 last updated on 13/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{Z},\:\mathrm{suppose}\:\mathrm{that}\:\exists{x}\in\mathbb{R}\:\mathrm{and} \\ $$$$\exists{y}\in\mathbb{R}\:\mathrm{with}\:{x}\neq{y}\:\mathrm{such}\:{f}\left({x}\right)\neq{f}\left({y}\right) \\ $$$$\mathrm{can}\:{f}\left({x}\right)\:\mathrm{be}\:\mathrm{conrinuous}? \\ $$ Answered by prakash jain last updated on 14/Jul/15 $${f}\left({x}\right)={a}\in\mathbb{Z}…

Question-132265

Question Number 132265 by Salman_Abir last updated on 12/Feb/21 Answered by physicstutes last updated on 12/Feb/21 $$\mathrm{m}\:=\:\mathrm{4}\:\mathrm{kg},\:{k}\:=\:\mathrm{100}\:\mathrm{Nm}^{−\mathrm{1}} \\ $$$$\:{T}\:=\:\mathrm{2}\pi\sqrt{\frac{{m}}{{k}}}\:=\:\mathrm{2}\pi\sqrt{\frac{\mathrm{4}}{\mathrm{100}}}\: \\ $$$$\Rightarrow\:{T}\:=\:\frac{\mathrm{4}\pi}{\mathrm{25}}\:\mathrm{s} \\ $$$${f}\:=\:\frac{\mathrm{1}}{{T}}\:=\:\frac{\mathrm{25}}{\mathrm{4}\pi}\:\mathrm{Hz} \\ $$$${T}\:=\:\frac{\mathrm{2}\pi}{\omega}\:\Rightarrow\:\omega\:=\:\frac{\mathrm{2}\pi}{{T}}\:\:=\:\mathrm{2}\pi\:.\:\frac{\mathrm{25}}{\mathrm{4}\pi}\:=\:\frac{\mathrm{25}}{\mathrm{2}}\:\mathrm{rad}/\mathrm{s}…

Question-132264

Question Number 132264 by Salman_Abir last updated on 12/Feb/21 Answered by physicstutes last updated on 12/Feb/21 $$\mathrm{frequency}\:=\:\mathrm{5}\:\mathrm{Hz} \\ $$$$\:\:\omega\:=\:\mathrm{2}\pi{f} \\ $$$$\Rightarrow\:\omega\:=\:\frac{\mathrm{2}\pi}{\mathrm{5}}\:\mathrm{rad}/\mathrm{s} \\ $$$$\:\mathrm{T}\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\mathrm{s} \\ $$…

lets-f-R-R-and-g-Z-R-such-that-f-x-g-x-x-Z-given-a-Z-then-proof-or-give-a-counter-example-that-lim-x-a-f-x-g-a-

Question Number 1192 by 123456 last updated on 13/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{and}\:{g}:\mathbb{Z}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}\right)={g}\left({x}\right),{x}\in\mathbb{Z} \\ $$$$\mathrm{given}\:{a}\in\mathbb{Z},\:\mathrm{then}\:\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)={g}\left({a}\right) \\ $$ Commented by prakash jain last updated…

Question-132261

Question Number 132261 by muneer0o0 last updated on 12/Feb/21 Answered by Olaf last updated on 13/Feb/21 $$\Omega\:=\:\int_{−\mathrm{1}} ^{+\mathrm{1}} \int_{−\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} ^{+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \mathrm{sec}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}…

Question-132260

Question Number 132260 by Salman_Abir last updated on 12/Feb/21 Answered by Olaf last updated on 13/Feb/21 $$\left({x}\sqrt{{x}}\right)^{{x}} \:=\:{x}^{{x}\sqrt{{x}}} \\ $$$$\left({x}^{\mathrm{3}/\mathrm{2}} \right)^{{x}} \:=\:{x}^{{x}^{\mathrm{3}/\mathrm{2}} } \\ $$$${x}\mathrm{ln}{x}^{\mathrm{3}/\mathrm{2}}…