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Question-209540

Question Number 209540 by mokys last updated on 13/Jul/24 Answered by Spillover last updated on 13/Jul/24 $$\int\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{6}} {x}+\mathrm{sin}\:^{\mathrm{5}} {x}+\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}} \\ $$$$\mathrm{sin}\:^{\mathrm{6}} {x}+\mathrm{sin}\:^{\mathrm{5}}…

dx-x-4-4-

Question Number 209543 by Spillover last updated on 13/Jul/24 $$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{4}} \\ $$$$ \\ $$ Commented by Frix last updated on 14/Jul/24 $$\mathrm{Done}\:\mathrm{several}\:\mathrm{times}\:\mathrm{before}…

If-a-n-is-absolutely-convergent-prove-that-a-n-n-is-also-absolutely-convergent-

Question Number 209514 by depressiveshrek last updated on 12/Jul/24 $$\mathrm{If}\:\Sigma\:{a}_{{n}} \:\mathrm{is}\:\mathrm{absolutely}\:\mathrm{convergent},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\Sigma\:\frac{{a}_{{n}} }{{n}}\:\mathrm{is}\:\mathrm{also}\:\mathrm{absolutely}\:\mathrm{convergent}. \\ $$ Answered by MM42 last updated on 13/Jul/24 $$\frac{\mid{a}_{{n}} \mid}{{n}}\:<\mid{a}_{{n}}…

At-what-value-of-a-does-the-system-of-equations-have-4-solutions-x-2-y-2-0-x-a-2-y-2-1-

Question Number 209520 by Ismoiljon_008 last updated on 12/Jul/24 $$ \\ $$$$\:\:\:{At}\:{what}\:{value}\:{of}\:\:{a}\:{does}\:{the}\:{system} \\ $$$$\:\:\:{of}\:{equations}\:{have}\:\mathrm{4}\:{solutions}\:? \\ $$$$\:\:\:\left\{\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{0}\right. \\ $$$$\:\:\:\left\{\left({x}−{a}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right. \\ $$$$ \\…