Question Number 21223 by moadakennaf last updated on 16/Sep/17 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\pi−\mathrm{2}{x}\right)\mathrm{tan}\:\left({x}\right) \\ $$ Answered by dioph last updated on 16/Sep/17 $$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\pi−\mathrm{2}{x}}{\mathrm{cot}\:{x}}\:= \\ $$$$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{−\mathrm{2}}{−\mathrm{cosec}^{\mathrm{2}}…
Question Number 21219 by Tinkutara last updated on 16/Sep/17 $$\left(\mathrm{A}\right)\:\mathrm{If}\:\mid{w}\mid\:=\:\mathrm{2},\:\mathrm{then}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points} \\ $$$${z}\:=\:{w}\:−\:\frac{\mathrm{1}}{{w}}\:\mathrm{is}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{If}\:\mid{w}\mid\:=\:\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points} \\ $$$${z}\:=\:{w}\:+\:\frac{\mathrm{1}}{{w}}\:\mathrm{is}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{Options}\:\mathrm{for}\:\mathrm{both}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}: \\ $$$$\left(\mathrm{p}\right)\:\mathrm{An}\:\mathrm{ellipse}\:\mathrm{with}\:\mathrm{eccentricity}\:\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\left(\mathrm{q}\right)\:\mathrm{The}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:{z}\:\mathrm{satisfying}\:\mathrm{Im}\:{z} \\ $$$$=\:\mathrm{0} \\…
Question Number 152291 by iloveisrael last updated on 27/Aug/21 $$\:\int\:\frac{{dx}}{\mathrm{cos}\:{x}+\mathrm{cosec}\:{x}}\:=? \\ $$ Answered by puissant last updated on 27/Aug/21 $${I}=\int\frac{{dx}}{{cosx}+{cosecx}} \\ $$$$=\int\frac{{sinx}}{{cosxsinx}+\mathrm{1}}{dx}\:=\:\int\frac{\mathrm{2}{sinx}}{{sin}\mathrm{2}{x}+\mathrm{2}}{dx} \\ $$$$=\int\frac{{sinx}+{cosx}}{{sin}\mathrm{2}{x}+\mathrm{2}}{dx}+\int\frac{{sinx}−{cosx}}{{sin}\mathrm{2}{x}+\mathrm{2}}{dx} \\…
Question Number 152287 by john_santu last updated on 27/Aug/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)^{\frac{\mathrm{6}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}} \:=? \\ $$ Answered by iloveisrael last updated on 27/Aug/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}}…
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Question Number 152281 by john_santu last updated on 27/Aug/21 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{triple}\:\mathrm{of}\:\mathrm{rational}\: \\ $$$$\mathrm{numbers}\:\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\sqrt[{\mathrm{3}}]{\sqrt[{\mathrm{3}}]{\mathrm{2}}−\mathrm{1}}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{a}}\:+\sqrt[{\mathrm{3}}]{\mathrm{b}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{c}}\: \\ $$ Answered by puissant last updated on 27/Aug/21 $${t}=\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\Rightarrow\:{t}^{\mathrm{3}} =\mathrm{2}\:\rightarrow\:{t}^{\mathrm{3}}…
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Question Number 152276 by peter frank last updated on 27/Aug/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{xtan}\:\mathrm{x}}{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\mathrm{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}}−\pi \\ $$ Answered by Olaf_Thorendsen last updated on 27/Aug/21…
Question Number 21205 by virus last updated on 15/Sep/17 Commented by virus last updated on 15/Sep/17 $${please}\:{solve}\:{it}\:{fast} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 86741 by M±th+et£s last updated on 30/Mar/20 $$\begin{cases}{{x}+\mathrm{10}{y}+\mathrm{50}{z}=\mathrm{500}}\\{{x}+{y}+{z}=\mathrm{100}}\end{cases} \\ $$$$ \\ $$$${find}\:{x},{y},{z} \\ $$ Commented by mr W last updated on 30/Mar/20 $${x},{y},{z}\in{N}\:?…