Question Number 73231 by mathmax by abdo last updated on 08/Nov/19 $${find}\:{the}\:{sum}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \left({n}^{\mathrm{2}} −\mathrm{3}{n}+\mathrm{1}\right){e}^{−{n}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 138767 by bramlexs22 last updated on 18/Apr/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{sin}\:^{\mathrm{2}} {x}\right)}\:=? \\ $$ Answered by EDWIN88 last updated on 18/Apr/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{sin}\:^{\mathrm{2}}…
Question Number 138766 by nadovic last updated on 18/Apr/21 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} +{x}+\mathrm{2}=\mathrm{0},\:\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{whose} \\ $$$$\mathrm{roots}\:\mathrm{are}\:\:\frac{\mathrm{1}}{\alpha^{\mathrm{2}} }\:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\beta^{\mathrm{2}} }\:\:\mathrm{and}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{27}\alpha^{\mathrm{4}} =\mathrm{11}\alpha+\mathrm{10}. \\ $$ Commented by MJS_new…
Question Number 7692 by Rohit last updated on 09/Sep/16 $${d}\:{efine}\:{the}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{5}} {\sum}}\:{a}_{{i}} \:=\mathrm{10}\:\:\:\Sigma\:{kya}\:{hai} \\ $$ Answered by prakash jain last updated on 11/Sep/16 $$\Sigma\:\mathrm{stands}\:\mathrm{for}\:\mathrm{summation}\:\mathrm{notation}. \\…
Question Number 73227 by mathmax by abdo last updated on 08/Nov/19 $${find}\:{the}\:{polynom}\:{T}_{{n}} \:{wich}\:{verify}\:{T}_{{n}} \left({cos}\theta\right)={cos}\left({n}\theta\right) \\ $$$$\forall{n}\:{integr}\:\forall\theta\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{T}_{\mathrm{0}} ,{T}_{\mathrm{1}} {and}\:{T}_{\mathrm{2}} {and}\:{prove}\:{that}\: \\ $$$${T}_{{n}+\mathrm{2}} =\mathrm{2}{x}\:{T}_{{n}+\mathrm{1}} −{T}_{{n}}…
Question Number 138763 by mathsuji last updated on 17/Apr/21 $${Make}\:{arbitrary}\:{movements}\:{between} \\ $$$${the}\:\mathrm{7}\:{people}\:{sitting}\:{around}\:{the}\:{table} \\ $$$${so}\:{that}\:{at}\:{least}\:{one}\:{of}\:{the}\:{people}\:{sitting} \\ $$$${next}\:{to}\:{you}\:{is}\:{not}\:{a}\:{Mathematician}.. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73224 by mr W last updated on 09/Nov/19 $${find}\:{the}\:{coefficient}\:{a}_{{k}} \:{of}\:{term}\:{x}^{{k}} \:{in} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+{x}^{{r}} \right)\:{with}\:\mathrm{0}\leqslant{k}\leqslant\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$$$ \\ $$$${example}:\:{n}=\mathrm{100},\:{k}=\mathrm{50} \\ $$ Answered…
Question Number 73225 by mathmax by abdo last updated on 08/Nov/19 $${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} −\mathrm{2}{xcos}\theta\:+\mathrm{1}\right){d}\theta\:\:{with}\:{x}\:{real}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73222 by Tanmay chaudhury last updated on 08/Nov/19 Answered by Tanmay chaudhury last updated on 08/Nov/19 $$\left[\overset{\rightarrow} {{a}}\overset{\rightarrow} {{b}}\overset{\rightarrow} {{c}}\right]=\mathrm{2}=\left(\overset{\rightarrow} {{a}}×\overset{\rightarrow} {{b}}\right).\overset{\rightarrow} {{c}}…
Question Number 138756 by 676597498 last updated on 17/Apr/21 $${show}\:{that} \\ $$$$\mathrm{0}\:\leqslant\:\left(\int_{\mathrm{0}} ^{\:\mathrm{2}} \left(\frac{\left(\mathrm{2}−{x}\right)^{{n}} {e}^{{x}} }{{n}!}{dx}\right)\right)\:\leqslant\:\frac{\mathrm{2}^{{n}} \left({e}^{\mathrm{2}} −\mathrm{1}\right)}{{n}!} \\ $$ Answered by mr W last…