Question Number 132226 by kaivan.ahmadi last updated on 12/Feb/21 $${li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\:\:{xln}\left({sinx}\right) \\ $$ Answered by Olaf last updated on 12/Feb/21 $$\mathrm{sin}{x}\:\underset{\mathrm{0}} {\sim}\:{x} \\ $$$$\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 1151 by 123456 last updated on 05/Jul/15 $$\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 132220 by aurpeyz last updated on 12/Feb/21 Answered by Olaf last updated on 12/Feb/21 $$\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6}\left(\mathrm{cos60}°\overset{\rightarrow} {{i}}+\mathrm{sin60}°\overset{\rightarrow} {{j}}\right) \\ $$$$\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6}\left(\frac{\mathrm{1}}{\mathrm{2}}\overset{\rightarrow} {{i}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\overset{\rightarrow} {{j}}\right)…
Question Number 66684 by Tinkutara@ last updated on 18/Aug/19 Answered by MJS last updated on 18/Aug/19 $$\mathrm{this}\:\mathrm{is}\:\mathrm{old}… \\ $$$$\mathrm{you}\:\mathrm{always}\:\mathrm{say}\:\mathrm{in}\:\mathrm{words}\:\mathrm{what}\:\mathrm{you}\:\mathrm{read}\:\mathrm{and} \\ $$$$\mathrm{write}\:\mathrm{down}\:\mathrm{in}\:\mathrm{numbers} \\ $$$$\mathrm{1} \\ $$$$\mathrm{one}\:“\mathrm{1}''\:=\:\mathrm{1}\:\mathrm{1}…
Question Number 1147 by prakash jain last updated on 04/Jul/15 $${f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$$${f}\left(\mathrm{0}\right)=? \\ $$ Commented by prakash jain last updated on 04/Jul/15 $${f}\left({f}\left(\mathrm{0}\right)\right)=\mathrm{1}…
Question Number 66683 by Tinkutara@ last updated on 18/Aug/19 Commented by mr W last updated on 18/Aug/19 $${each}\:{runner}\:{has}\:{two}\:{possibilities},\:{totally} \\ $$$$\mathrm{2}×\mathrm{2}×\mathrm{2}=\mathrm{8}.\:{such}\:{that}\:{they}\:{don}'{t}\:{collide}, \\ $$$${all}\:{of}\:{them}\:{must}\:{run}\:{in}\:{the}\:{same} \\ $$$${direction},\:{there}\:{are}\:{two}\:{such}\:{possibilities}. \\…
Question Number 66680 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{2}^{{n}} }{\mathrm{3}^{{n}} \left(\mathrm{2}{n}^{\mathrm{3}} \:+{n}^{\mathrm{2}} −\mathrm{5}{n}\:+\mathrm{2}\right)} \\ $$ Commented by Mohamed Amine Bouguezzoul…
Question Number 66681 by Tinkutara@ last updated on 18/Aug/19 Commented by Tinkutara@ last updated on 18/Aug/19 $$?? \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 1139 by 314159 last updated on 30/Jun/15 $${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 132211 by benjo_mathlover last updated on 12/Feb/21 $$ \\ $$$$\mathrm{how}\:\mathrm{fast}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\: \\ $$$$\mathrm{rectangle}\:\mathrm{changing}\:\mathrm{if}\:\mathrm{one}\:\mathrm{side}\:\mathrm{is}\:\mathrm{10} \\ $$$$\:\mathrm{cm}\:\mathrm{long}\:\mathrm{and}\:\mathrm{increasing}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{rate}\:\mathrm{of}\:\mathrm{2}\:\mathrm{cm}/\mathrm{s}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{side}\:\mathrm{is}\: \\ $$$$\mathrm{8}\:\mathrm{cm}\:\mathrm{long}\:\mathrm{and}\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{at}\: \\ $$$$\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{3}\:\mathrm{cm}/\mathrm{s} \\ $$ Answered…