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 $${f}\left({x}\right)={a}\in\mathbb{Z}…
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Question Number 1192 by 123456 last updated on 13/Jul/15 $$\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…
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Question Number 1155 by 123456 last updated on 05/Jul/15 $$\mathrm{what}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{60}{x}+\mathrm{120}{y}+\mathrm{1250}{z} \\ $$$$\mathrm{if} \\ $$$${x}+{y}+\mathrm{5}{z}=\mathrm{150} \\ $$$${x}\in\left\{\mathrm{0},…,\mathrm{150}\right\} \\ $$$${y}\in\left\{\mathrm{0},…,\mathrm{150}\right\} \\ $$$${z}\in\left\{\mathrm{0},…,\mathrm{30}\right\} \\ $$ Answered…
Question Number 1151 by 123456 last updated on 05/Jul/15 $$\mathrm{what}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{60}{x}+\mathrm{120}{y} \\ $$$$\mathrm{where} \\ $$$${x}+{y}=\mathrm{150} \\ $$$${x}\in\left\{\mathrm{0},\mathrm{1},…,\mathrm{150}\right\} \\ $$$${y}\in\left\{\mathrm{0},\mathrm{1},…,\mathrm{150}\right\} \\ $$ Answered by prakash…
Question Number 1139 by 314159 last updated on 30/Jun/15 $${Given}\:{that}\:{f}\:{is}\:{a}\:{polynomial}\:{function}\:{of} \\ $$$${degree}\:\mathrm{8}\:{such}\:{that}\:{f}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}},{f}\left(\mathrm{2}\right)=\frac{\mathrm{1}}{\mathrm{6}},{f}\left(\mathrm{3}\right)=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$${f}\left(\mathrm{4}\right)=\frac{\mathrm{1}}{\mathrm{20}},{f}\left(\mathrm{5}\right)=\frac{\mathrm{1}}{\mathrm{30}},{f}\left(\mathrm{6}\right)=\frac{\mathrm{1}}{\mathrm{42}},{f}\left(\mathrm{7}\right)=\frac{\mathrm{1}}{\mathrm{56}},{f}\left(\mathrm{8}\right)=\frac{\mathrm{1}}{\mathrm{72}} \\ $$$${f}\left(\mathrm{9}\right)=\frac{\mathrm{1}}{\mathrm{90}\:}\:\:.{Find}\:{f}\left(\mathrm{10}\right)\:{and}\:{f}\left(\mathrm{11}\right). \\ $$ Commented by 123456 last updated on 30/Jun/15…
Question Number 1134 by 314159 last updated on 28/Jun/15 $${Find}\:{the}\:{infinite}\:{product}\:{of}\: \\ $$$$\frac{\mathrm{3}}{\mathrm{2}}×\frac{\mathrm{5}}{\mathrm{4}}×\frac{\mathrm{17}}{\mathrm{16}}×\frac{\mathrm{257}}{\mathrm{256}}×\frac{\mathrm{65537}}{\mathrm{65536}}×… \\ $$ Answered by prakash jain last updated on 29/Jun/15 $$\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{2}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}^{\mathrm{2}}…
Question Number 132173 by I want to learn more last updated on 11/Feb/21 $$\mathrm{If}\:\:\:\:\mathrm{v}\:\:\:=\:\:\:\frac{\sqrt{\mathrm{p}\:\:\:+\:\:\:\frac{\mathrm{1}}{\mathrm{n}}}}{\mathrm{x}},\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\:\:\mathrm{p}\:\:=\:\:\:\mathrm{pressure}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\:\:\:\:\mathrm{n}\:\:\:\mathrm{and}\:\:\:\mathrm{x} \\ $$ Commented by mr W last updated on…
Question Number 132162 by Dwaipayan Shikari last updated on 11/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$ Answered by mnjuly1970 last updated on 11/Feb/21 $$\frac{\mathrm{1}}{\mathrm{2}{i}}\left[{li}_{\mathrm{2}} \left({e}^{{i}}…