Question Number 1468 by havandip last updated on 11/Aug/15 $$ \\ $$ Answered by 123456 last updated on 11/Aug/15 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)=\mathrm{L} \\ $$$$\forall\epsilon>\mathrm{0},\exists\mathrm{M}\in\mathbb{R},\forall{x}<\mathrm{M},\mid{f}\left({x}\right)−\mathrm{L}\mid<\epsilon \\ $$…
Question Number 132439 by liberty last updated on 14/Feb/21 $$ \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{particular} \\ $$$$\mathrm{machine}\:\mathrm{will}\:\mathrm{make}\:\mathrm{product}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{90\%}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{well},\:\:\mathrm{but}\:\mathrm{will}\:\mathrm{do}\:\mathrm{so}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\:\mathrm{rate}\:\mathrm{of}\:\mathrm{only}\:\mathrm{30\%}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{running}\:\mathrm{well}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{machine}\:\mathrm{is}\: \\…
Question Number 132382 by liberty last updated on 13/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{x}^{\mathrm{10}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{8}} \\ $$ Answered by EDWIN88 last updated on 13/Feb/21 $$\mathrm{by}\:\mathrm{multinomial}\:\mathrm{theorem}\:;\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{10}} \\…
Question Number 132174 by EDWIN88 last updated on 12/Feb/21 Commented by EDWIN88 last updated on 12/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Commented by mr W last updated…
Question Number 1074 by Yugi last updated on 05/Jun/15 $${Prove}\:{by}\:{induction}\:{the}\:{following}\:{result}\:{where}\:{N}\:{is}\:{a}\:{positive}\:{even}\:{integer}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}_{\mathrm{1}} ^{\mathrm{2}} +{S}_{\mathrm{2}} ^{\mathrm{2}} =\mathrm{2}^{{N}} \\ $$$${where}\:\:\:\:{S}_{\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{\frac{{N}}{\mathrm{2}}+\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \begin{pmatrix}{{N}}\\{\mathrm{2}\left({r}−\mathrm{1}\right)}\end{pmatrix}\:\:\:\:{and}\:\:\:\:\:\:{S}_{\mathrm{2}} =\underset{{r}=\mathrm{1}} {\overset{{N}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{{r}+\mathrm{1}}…
Question Number 66549 by aditya@345 last updated on 17/Aug/19 $$\frac{\mathrm{n}^{\mathrm{2}} !}{\left(\mathrm{n}!\right)^{\mathrm{n}} }=\mathrm{natural}\:\mathrm{number}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131994 by liberty last updated on 10/Feb/21 Commented by liberty last updated on 10/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Answered by EDWIN88 last updated on…
Question Number 921 by 112358 last updated on 24/Apr/15 $${How}\:{many}\:{arrays}\:{of}\:{the}\:{letters} \\ $$$${of}\:{the}\:{word}\:{BELMOPAN}\:{are}\: \\ $$$${possible}\:{if}\:{no}\:{two}\:{vowels}\:{come} \\ $$$${together}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 911 by 112358 last updated on 22/Apr/15 $${Eight}\:{people}\:{are}\:{seated}\:{around} \\ $$$${a}\:{circular}\:{table}.\:{Each}\:{person} \\ $$$${must}\:{shake}\:{everyone}'{s}\:{hand}\:{but} \\ $$$${they}\:{must}\:{not}\:{shake}\:{hands}\:{with} \\ $$$${the}\:{two}\:{persons}\:{seated}\:{at}\:{their}\:{sides}. \\ $$$${How}\:{many}\:{handshakes}\:{occur}? \\ $$ Answered by prakash…
Question Number 883 by 112358 last updated on 12/Apr/15 $${How}\:{many}\:{even}\:{numbers}\: \\ $$$${between}\:\mathrm{3000}\:{and}\:\mathrm{7000}\:{can}\:{be} \\ $$$${formed}\:{using}\:{the}\:{digits}\: \\ $$$$\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:{and}\:\mathrm{8}\:{if}\:{repetition} \\ $$$${of}\:{digits}\:{is}\:{not}\:{allowed}? \\ $$ Answered by prakash jain last…