Question Number 7541 by 314159 last updated on 03/Sep/16 Commented by prakash jain last updated on 03/Sep/16 $${a}\left(\mathrm{1}+{r}+{r}^{\mathrm{2}} +{r}^{\mathrm{3}} +{r}^{\mathrm{4}} \right)=\mathrm{211} \\ $$$${a}\:{and}\:{r}\:{integers} \\ $$$$\mathrm{211}=\mathrm{1}×\mathrm{211}\Rightarrow{a}=\mathrm{1}…
Question Number 138608 by Dwaipayan Shikari last updated on 15/Apr/21 $${Prove}\:{or}\:{disprove} \\ $$$$\int_{\mathrm{0}} ^{{a}} {x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\mathrm{1}}{{e}^{{a}^{\mathrm{2}} } }\left(\frac{{a}^{\mathrm{3}} }{\mathrm{1}.\mathrm{3}}+\frac{\mathrm{2}{a}^{\mathrm{5}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}}+\frac{\mathrm{2}{a}^{\mathrm{7}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}}+\frac{\mathrm{2}{a}^{\mathrm{9}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}.\mathrm{9}}+{ad}\:{inf}..\right) \\…
Question Number 7538 by 2402@gmail.com last updated on 02/Sep/16 $${Q}.\:\int\frac{\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}{{x}^{\mathrm{2}} −\mathrm{1}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138611 by liberty last updated on 15/Apr/21 $${Given}\:{a}\:{function}\:{f}\:{where}\: \\ $$$${f}\left({x}\right)\geqslant\:\mathrm{0}{for}\:\forall{x}\in\mathbb{R}.\:{If}\:{the}\:{area} \\ $$$${U}\:=\:\left\{\:\left({x},{y}\right)\mid\mathrm{0}\leqslant\mathrm{2}{y}\leqslant{f}\left({x}\right),\:−\mathrm{6}\leqslant{x}\leqslant−\mathrm{2}\right\} \\ $$$${is}\:{u}\:{and}\:{the}\:{area}\:{V}=\left\{\left({x},{y}\right)\mid\mathrm{0}\leqslant{y}\leqslant{f}\left({x}\right),−\mathrm{2}\leqslant{x}\leqslant\mathrm{0}\right\} \\ $$$${is}\:{v}\:{then}\:{what}\:{the}\:{value}\:{of} \\ $$$$\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\mathrm{4}{x}\:{f}\left(\mathrm{2}{x}^{\mathrm{2}} −\mathrm{8}\right)\:{dx}\:. \\ $$$$\left({A}\right)\:\mathrm{5}{u}+\mathrm{4}{v}\:\:\:\:\:\left({D}\right)\mathrm{2}{u}+{v}…
Question Number 7532 by Yozzia last updated on 02/Sep/16 $${Find}\:{x}_{{n}} \:\left({n}\in\mathbb{Z}\right)\:{satisfying}\:{x}_{\mathrm{0}} =\mathrm{0},\:{x}_{\mathrm{1}} =\mathrm{1}\:{and} \\ $$$${x}_{{n}+\mathrm{1}} ={x}_{{n}} \sqrt{{x}_{{n}−\mathrm{1}} ^{\mathrm{2}} +\mathrm{1}}+{x}_{{n}−\mathrm{1}} \sqrt{{x}_{{n}} ^{\mathrm{2}} +\mathrm{1}}\:{for}\:{n}\geqslant\mathrm{1}. \\ $$ Commented…
Question Number 138600 by Raxreedoroid last updated on 15/Apr/21 $$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({k}\right)={f}\left(\mathrm{1}\right)+\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\left(\frac{\underset{{i}=\mathrm{1}} {\overset{{k}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {f}\left({i}+\mathrm{1}\right){C}_{{i}−\mathrm{1}} ^{{k}−\mathrm{2}} }{\left({k}−\mathrm{1}\right)!}\:\underset{{i}=\mathrm{1}} {\overset{{k}−\mathrm{1}} {\prod}}\left({n}−{i}\right)\right) \\ $$…
Question Number 138603 by Ar Brandon last updated on 15/Apr/21 $$\frac{\mathrm{1}}{\mathrm{2}\pi\mathrm{i}}\underset{\mathrm{T}\rightarrow\infty} {\mathrm{lim}}\underset{\gamma−\mathrm{iT}} {\overset{\gamma+\mathrm{iT}} {\int}}\frac{\mathrm{e}^{\mathrm{st}} }{\mathrm{s}−\mathrm{a}}\mathrm{ds} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138598 by qaz last updated on 15/Apr/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!\left(\mathrm{2}{n}+\mathrm{3}\right)}\left(\frac{\mathrm{4}}{\pi}\right)^{{n}} =? \\ $$ Answered by mr W last updated on 15/Apr/21 $${e}^{{x}}…
Question Number 73059 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} \left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{fartorize}\:{inside}\:{C}\left({x}\right)\:{P}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\prod_{{k}=\mathrm{1}} ^{{p}} \:{cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right) \\ $$ Commented by…
Question Number 73056 by mathmax by abdo last updated on 05/Nov/19 $${if}\:\left({xsina}+{cosa}\right)^{{n}} ={q}\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)+{r}\:{find}\:{r} \\ $$ Commented by mathmax by abdo last updated on 06/Nov/19…