Question Number 1397 by 314159 last updated on 28/Jul/15 $${Arrange}\:\mathrm{8}\:{coins}\:{in}\:{one}\:{line}\:{on}\:{a}\:{table} \\ $$$${such}\:{that}\:{the}\:{head}\:{or}\:{tail}\:{will}\:{be}\:{facing} \\ $$$${upward}.{Try}\:{to}\:{flip}\:{two}\:{neighboring}\:{coins}\: \\ $$$${that}\:{are}\:{not}\:{with}\:{identical}\:{face}\:{upside}\:{down}.{After}\: \\ $$$${several}\:{operations}\:,\:{how}\:{many}\:{different}\: \\ $$$${ways}\:{can}\:{the}\:{heads}\:{and}\:{tails}\:{be}\:{arranged} \\ $$$${in}\:{one}\:{line}\:{on}\:{the}\:{table}. \\ $$ Commented…
Question Number 66932 by Tinkutara@ last updated on 20/Aug/19 $${which}\:{of}\:{the}\:{sequences}\:{converges}\:? \\ $$$$\left.\mathrm{1}\right)\:{a}_{{n}} =\:{n}−\frac{\mathrm{1}}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{a}_{{n}} =\:\left(\left(−\mathrm{1}\right)^{{n}} +\mathrm{1}\right)\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$ Answered by turbo msup by abdo…
Question Number 1379 by 314159 last updated on 27/Jul/15 $${Find}\:{all}\:{positive}\:{integers}\:{n}\:{such}\:{that}\:\: \\ $$$${n}\leqslant\mathrm{2014}\:{and}\:\mathrm{3}^{{n}−\mathrm{1}} .{n}\:\:{will}\:{be}\:{a}\:{perfect}\:{square}\:{integer}. \\ $$ Commented by 123456 last updated on 26/Jul/15 $${m}\equiv\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$${n}={m}^{\mathrm{2}}…
Question Number 1375 by 123456 last updated on 26/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{and}\:{g}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{two}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differentiable}\:\mathrm{functions} \\ $$$$\mathrm{suppose}\:\mathrm{that}\:{g}\left(\mathrm{0}\right)=\mathrm{0},\:\mathrm{then}\:\mathrm{compute} \\ $$$${h}\left({x}\right)=\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{g}\left({f}\left({x}+\Delta{x}\right)−{f}\left({x}\right)\right)}{\Delta{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1369 by 123456 last updated on 25/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differentiable} \\ $$$$\mathrm{compute} \\ $$$${g}\left({x}\right)=\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{{f}\left({x}+\Delta{x}\right)} −{e}^{{f}\left({x}\right)} }{{f}\left({x}+\Delta{x}\right)−{f}\left({x}\right)} \\ $$ Answered by prakash jain last updated…
Question Number 132434 by Dwaipayan Shikari last updated on 14/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$ Answered by mnjuly1970 last updated on 14/Feb/21 $$\:\:{solution}: \\…
Question Number 1339 by 123456 last updated on 24/Jul/15 $${f}:\mathbb{C}\rightarrow\mathbb{C},{z}_{\mathrm{0}} \in\mathbb{C}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({z}\right)−{f}\left({z}_{\mathrm{0}} \right)=\left({z}−{z}_{\mathrm{0}} \right){f}\left({z}−{z}_{\mathrm{0}} \right) \\ $$$$\mathrm{does}\:\underset{{z}\rightarrow{z}_{\mathrm{0}} } {\mathrm{lim}}{f}\left({z}\right)={f}\left({z}_{\mathrm{0}} \right)? \\ $$ Commented by…
Question Number 1335 by 123456 last updated on 23/Jul/15 $$\mathrm{if}\:{a}\leqslant{x}\leqslant{b}\:\mathrm{and}\:{c}\leqslant{y}\leqslant{d}\:\mathrm{then}\:\mathrm{did} \\ $$$$\frac{{a}}{{d}}\leqslant\frac{{x}}{{y}}\leqslant\frac{{b}}{{c}}? \\ $$$${a},{b},{c},{d},{x},{y}\in\mathbb{R} \\ $$$$\mathrm{0}<{c} \\ $$$$\mathrm{0}<{a} \\ $$ Answered by prakash jain last…
Question Number 66868 by John Kaloki Musau last updated on 20/Aug/19 $${A}\:{town}\:{N}\:{is}\:\mathrm{340}{km}\:{due}\:{west}\:{of}\: \\ $$$${town}\:{G}\:{and}\:{town}\:{K}\:{is}\:{due}\:{west}\: \\ $$$${of}\:{town}\:{N}.\:{A}\:{helicopter}\:{Zebra}\: \\ $$$${left}\:{G}\:{for}\:{K}\:{at}\:\mathrm{9}{a}.{m}.\:{Another}\: \\ $$$${helicopter}\:{Buffalo}\:{left}\:{N}\:{for}\:{K} \\ $$$${at}\:\mathrm{11}{a}.{m}.\:{Helicopter}\:{Buffalo} \\ $$$${travelled}\:{at}\:{an}\:{average}\:{speed}\:{of}\: \\…
Question Number 66865 by John Kaloki Musau last updated on 20/Aug/19 $${A}\:{and}\:{B}\:{are}\:{two}\:{towns}\:\mathrm{360}{km}\:{apart}. \\ $$$${An}\:{express}\:{bus}\:{departs}\:{from}\:{A}\:{at} \\ $$$$\mathrm{8}{a}.{m}\:{and}\:{maintains}\:{an}\:{average} \\ $$$${speed}\:{of}\:\mathrm{90}{km}/{h}\:{between}\:{A}\:{and}\:{B}. \\ $$$${Another}\:{bus}\:{starts}\:{from}\:{B}\:{also}\:{at} \\ $$$$\mathrm{8}{a}.{m}\:{and}\:{moves}\:{towards}\:{A}\:{making} \\ $$$${four}\:{stops}\:{at}\:{four}\:{equally}\:{spaced} \\…