Question Number 6267 by sanusihammed last updated on 21/Jun/16 $${Verify}\:{the}\:{convergence}\:{of}\:{the}\:{exponential}\:{series}\:\:{e}^{{x}} \\ $$$${using}\:{D}'{Alermbert}\:{ratio}\:{test}. \\ $$ Commented by Yozzii last updated on 21/Jun/16 $${u}_{{r}} =\frac{{x}^{{r}} }{{r}!}\Rightarrow\frac{{u}_{{r}+\mathrm{1}} }{{u}_{{r}}…
Question Number 137338 by liberty last updated on 01/Apr/21 $$\mathrm{Given}\:\frac{\mathrm{cos}\:\mathrm{8}\theta+\mathrm{6cos}\:\mathrm{6}\theta+\mathrm{13cos}\:\mathrm{4}\theta+\mathrm{8cos}\:\mathrm{2}\theta}{\mathrm{cos}\:\mathrm{7}\theta+\mathrm{5cos}\:\mathrm{5}\theta+\mathrm{8cos}\:\mathrm{3}\theta}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{2}\theta\:? \\ $$ Answered by EDWIN88 last updated on 01/Apr/21 $$\mathrm{consider}\:\mathrm{numerator} \\ $$$$\Leftrightarrow\:\mathrm{cos}\:\mathrm{8}\theta+\mathrm{cos}\:\mathrm{6}\theta+\mathrm{5}\left(\mathrm{cos}\:\mathrm{6}\theta+\mathrm{cos}\:\mathrm{4}\theta\right)+\mathrm{8}\left(\mathrm{cos}\:\mathrm{4}\theta+\mathrm{cos}\:\mathrm{2}\theta\right) \\…
Question Number 71801 by mathmax by abdo last updated on 20/Oct/19 $${find}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 71799 by mind is power last updated on 20/Oct/19 Answered by mind is power last updated on 20/Oct/19 $$\mathrm{posted}\:\mathrm{Quation}\:\mathrm{two}\:\mathrm{weeks}\:\mathrm{Ago}−\:\mathrm{nice}\:\mathrm{one}\: \\ $$ Answered by…
Question Number 137335 by liberty last updated on 01/Apr/21 $$ \\ $$P(x) = 3x^75 + 2x^14 – 3x^2 – 1. What is the remainder when…
Question Number 137328 by mnjuly1970 last updated on 01/Apr/21 Answered by Dwaipayan Shikari last updated on 01/Apr/21 $$−\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\mathrm{2}} \left({x}\right){log}\left({sinx}\right){dx}\:\:\:\:\:\: \\ $$$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}\left({sinx}\right)−\int_{\mathrm{0}}…
Question Number 6257 by 314159 last updated on 20/Jun/16 $${Given}\:{that}\:{a}\:{and}\:{b}\:{are}\:{positive}\:{real}\:{number} \\ $$$${such}\:{that}\:{b}<\mathrm{4}{a}+\mathrm{1},{show}\:{that}\:\frac{\mathrm{2}{a}+{b}}{\mathrm{4}{a}+\mathrm{1}}<\sqrt{\mathrm{4}{a}^{\mathrm{2}} +{b}}\:. \\ $$ Answered by Yozzii last updated on 20/Jun/16 $$\frac{\mathrm{2}{a}+{b}}{\mathrm{4}{a}+\mathrm{1}}<\sqrt{\mathrm{4}{a}^{\mathrm{2}} +{b}}\:\:\:\:\:\:{a},{b}>\mathrm{0} \\…
Question Number 71790 by jatin123 last updated on 20/Oct/19 Answered by $@ty@m123 last updated on 20/Oct/19 $$=\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{3}}{\mathrm{4}}×…..×\frac{\mathrm{98}}{\mathrm{99}}×\frac{\mathrm{99}}{\mathrm{100}} \\ $$$$=\frac{\mathrm{2}}{\mathrm{100}}=\frac{\mathrm{1}}{\mathrm{50}} \\ $$ Commented by jatin123 last…
Question Number 137324 by greg_ed last updated on 01/Apr/21 $$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{evaluate}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{one}}\:: \\ $$$$\mathrm{P}\:=\:\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{1958}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{1959}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{1960}}\right)…\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2017}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2018}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2019}}\right) \\ $$$$\boldsymbol{\mathrm{P}}\:=\:?\: \\ $$ Answered by som(math1967) last updated on 01/Apr/21 $${P}=\left(\frac{\mathrm{1959}}{\mathrm{1958}}\right)\left(\frac{\mathrm{1960}}{\mathrm{1959}}\right)\left(\frac{\mathrm{1961}}{\mathrm{1960}}\right)..\left(\frac{\mathrm{2019}}{\mathrm{2018}}\right)\left(\frac{\mathrm{2020}}{\mathrm{2019}}\right) \\…