Question Number 87371 by M±th+et£s last updated on 04/Apr/20 $$\int\frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{4}}{{x}^{\mathrm{8}} −{x}^{\mathrm{5}} +\mathrm{9}}{dx} \\ $$ Commented by M±th+et£s last updated on 04/Apr/20 $${why}\:{sir} \\…
Question Number 152907 by mathdanisur last updated on 03/Sep/21 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{form}: \\ $$$$\Omega=\left(\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{29}} −\mathrm{x}^{\mathrm{9}} }{\mathrm{x}^{\mathrm{40}} +\mathrm{1}}\:\mathrm{dx}\right)\left(\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{29}} −\mathrm{2x}^{\mathrm{9}} }{\mathrm{x}^{\mathrm{40}} +\mathrm{4}}\mathrm{dx}\right) \\ $$ Answered…
Question Number 87369 by ajfour last updated on 04/Apr/20 Commented by ajfour last updated on 04/Apr/20 $${I}\:{think},\:\frac{{R}}{{r}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:\:\:\:{only},\:{Sir}. \\ $$ Commented by ajfour last updated on…
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Question Number 152900 by SANOGO last updated on 03/Sep/21 Answered by mindispower last updated on 03/Sep/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}.\frac{\mathrm{1}}{{n}}.\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{{k}}{{n}+\mathrm{1}}\right)^{{a}} }{{n}^{\mathrm{2}} {a}+\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}}…
Question Number 152903 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{1}.\mathrm{a}\right).\:\overset{−} {\mathrm{x}}\:=\:\frac{\Sigma\mathrm{f}_{\mathrm{i}} .\mathrm{x}_{\mathrm{i}} }{\Sigma\mathrm{f}_{\mathrm{i}} }\: \\ $$$$\:=\frac{\mathrm{2}×\mathrm{14},\mathrm{5}+\mathrm{9}×\mathrm{18},\mathrm{5}+\mathrm{12}×\mathrm{22},\mathrm{5}+\mathrm{9}×\mathrm{26},\mathrm{5}+\mathrm{5}×\mathrm{30},\mathrm{5}+\mathrm{3}×\mathrm{34},\mathrm{5}}{\mathrm{2}+\mathrm{9}+\mathrm{12}+\mathrm{9}+\mathrm{5}+\mathrm{3}} \\ $$$$=\frac{\mathrm{29}+\mathrm{166},\mathrm{5}+\mathrm{270}+\mathrm{238},\mathrm{5}+\mathrm{152},\mathrm{5}+\mathrm{103},\mathrm{5}}{\mathrm{40}}…
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Question Number 21825 by Joel577 last updated on 05/Oct/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{simplest}\:\mathrm{form}\:\mathrm{of} \\ $$$$\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{2}^{{k}} \left[\mathrm{sin}^{\mathrm{2}} \:\left(\frac{\mathrm{2}{k}\pi}{\mathrm{3}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right] \\ $$ Commented by sma3l2996 last updated on 05/Oct/17…
Question Number 152898 by bobhans last updated on 02/Sep/21 Commented by mathdanisur last updated on 03/Sep/21 $$\mathrm{5x}^{\mathrm{5}} −\mathrm{23x}^{\mathrm{4}} +\mathrm{39x}^{\mathrm{3}} −\mathrm{33x}^{\mathrm{2}} +\mathrm{24x}=\mathrm{4}\:\Rightarrow\:=\mathrm{2} \\ $$ Commented by…
Question Number 87358 by john santu last updated on 04/Apr/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:\mathrm{y}\:\mathrm{for}\:\mathrm{which}? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{y}^{\mathrm{2}} +\mathrm{10y}−\mathrm{24}\:\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)}{\mathrm{y}^{\mathrm{2}} +\mathrm{10y}\:−\mathrm{24}\:\mathrm{sin}\:\left(\frac{\mathrm{2}}{\mathrm{x}}\right)}\: \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$ Terms of Service…