Question Number 52516 by tanmay.chaudhury50@gmail.com last updated on 09/Jan/19 $${find}\:{the}\:{value} \\ $$$${tan}\theta+\mathrm{2}{tan}\mathrm{2}\theta+\mathrm{2}^{\mathrm{2}} {tan}\mathrm{2}^{\mathrm{2}} \theta+\mathrm{2}^{\mathrm{3}} {tan}\mathrm{2}^{\mathrm{3}} \theta+..+\mathrm{2}^{{n}−\mathrm{1}} {tan}\mathrm{2}^{{n}−\mathrm{1}} \theta \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 52515 by tanmay.chaudhury50@gmail.com last updated on 09/Jan/19 $$\left.\mathrm{1}\right)\int_{\mathrm{0}} ^{\infty} \frac{{tan}^{−\mathrm{1}} \left({ax}\right)−{tan}^{−\mathrm{1}} \left({bx}\right)}{{x}}{dx} \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {sinx}}{{x}}{dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last…
Question Number 52499 by Joel578 last updated on 09/Jan/19 $$\mathrm{Let}\:{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{degree}\:\mathrm{polynomial}. \\ $$$$\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\:\int_{\mid{z}\mid=\mathrm{2}} \frac{{z}\:{f}\:'\left({z}\right)}{{f}\left({z}\right)}\:{dz}\:=\:\mathrm{0},\:\:\mathrm{and}\:\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\:\int_{\mid{z}\mid=\mathrm{2}} \frac{{z}^{\mathrm{2}} \:{f}\:'\left({z}\right)}{{f}\left({z}\right)}\:{dz}\:=\:−\mathrm{2} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{0}\right)\:=\:\mathrm{2017},\:\mathrm{find}\:\mathrm{explicit}\:\mathrm{form}\:\mathrm{of}\:{f}\left({z}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 117990 by Dwaipayan Shikari last updated on 14/Oct/20 $$\left(\mathrm{2}.\mathrm{3}.\mathrm{5}.\mathrm{7}.\mathrm{9}.\mathrm{11}.\mathrm{13}.\mathrm{17}……\infty\right)×\sqrt{\frac{\mathrm{6}}{\mathrm{3}.\mathrm{8}.\mathrm{24}.\mathrm{48}.\mathrm{80}.\mathrm{120}.\mathrm{168}.\mathrm{288}…..\infty}} \\ $$ Answered by Dwaipayan Shikari last updated on 14/Oct/20 $$\sqrt{\mathrm{6}}.\sqrt{\frac{\mathrm{2}^{\mathrm{2}} .\mathrm{3}^{\mathrm{2}} .\mathrm{5}^{\mathrm{2}} .\mathrm{7}^{\mathrm{2}}…
Question Number 117980 by Lordose last updated on 14/Oct/20 $$\mathrm{Where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{quiz}? \\ $$$$ \\ $$ Commented by Tinku Tara last updated on 14/Oct/20 $$\mathrm{Some}\:\mathrm{mistake}\:\mathrm{were}\:\mathrm{pointed}\:\mathrm{out} \\ $$$$\mathrm{in}\:\mathrm{question}\:\mathrm{and}\:\mathrm{answers}\:\mathrm{and}\:\mathrm{we}\:\mathrm{decided}\:\mathrm{to}\:…
Question Number 183465 by Mastermind last updated on 26/Dec/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{1}−\mathrm{2x}\right)\left(\mathrm{1}−\mathrm{x}\right). \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$ Answered by mr W last updated on…
Question Number 183464 by Mastermind last updated on 26/Dec/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{3x}\left(\mathrm{4}−\mathrm{x}\right) \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$ Answered by mr W last updated on…
Question Number 52349 by Tawa1 last updated on 06/Jan/19 $$\mathrm{Determine}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges}. \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$$$ \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}\:−\:\mathrm{1}} } \\ $$$$\:\:\: \\…
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Question Number 52268 by tanmay.chaudhury50@gmail.com last updated on 05/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jan/19 $${Ramanuj}\:{proved}…\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}…\infty=\frac{−\mathrm{1}}{\mathrm{12}} \\ $$ Commented by Abdo msup. last updated…