Question Number 193967 by Risandu last updated on 24/Jun/23 Answered by MM42 last updated on 24/Jun/23 $${lim}_{\theta\rightarrow\pi} \:\:\frac{\mathrm{4}{sin}\theta{cos}\theta\left({cos}\theta−{sin}\mathrm{3}\theta\right)}{\left(\pi−\theta\right)\left(\pi+\theta\right)} \\ $$$${let}\:\:\:\:\theta=\pi−{u} \\ $$$$\Rightarrow{lim}_{{u}\rightarrow\mathrm{0}} \:\frac{−\mathrm{4}{sinu}×{cosu}×\left({sin}\mathrm{3}{u}−{cosu}\right)}{{u}×\left(\mathrm{2}\pi−{u}\right)} \\ $$$$\:=\frac{\mathrm{2}}{\pi}\:\checkmark…
Question Number 193874 by cortano12 last updated on 22/Jun/23 Answered by Subhi last updated on 22/Jun/23 $$ \\ $$$${cos}\left({y}\right)=\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \left(\frac{{y}}{\mathrm{2}}\right) \\ $$$$\mathrm{1}−{cos}\left({cx}^{\mathrm{2}} +{bx}+{a}\right)=\mathrm{2}{sin}^{\mathrm{2}} \left(\frac{{cx}^{\mathrm{2}} +{bx}+{a}}{\mathrm{2}}\right)…
Question Number 193863 by horsebrand11 last updated on 21/Jun/23 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} −\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)}{\mathrm{x}^{\mathrm{4}} }\:=? \\ $$ Answered by MM42 last updated on 21/Jun/23 $${u}\rightarrow\mathrm{0}\Rightarrow\mathrm{1}−{cosu}\:\sim\:\frac{\mathrm{1}}{\mathrm{2}}{u}^{\mathrm{2}} \\…
Question Number 193819 by SaRahAli last updated on 20/Jun/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\left(\frac{\frac{\Pi}{\mathrm{3}}+{x}}{{x}}\right) \\ $$ Answered by MM42 last updated on 20/Jun/23 $${not}\:{available} \\ $$ Terms of…
Question Number 193803 by cortano12 last updated on 20/Jun/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{11}−\mathrm{x}}\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{x}−\mathrm{2}}\right)}{\mathrm{cot}\:\left(\mathrm{x}−\mathrm{2}\right)}=? \\ $$ Answered by horsebrand11 last updated on 20/Jun/23 $$\:=\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{3}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\frac{\pi}{\mathrm{x}−\mathrm{2}}\right)}{\mathrm{cot}\:\left(\mathrm{x}−\mathrm{2}\right)} \\ $$$$\:=\:\mathrm{3}\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\mathrm{sin}\:\left(\mathrm{x}−\mathrm{2}\right)\:\mathrm{sin}\:\pi\left(\frac{\mathrm{x}−\mathrm{4}}{\mathrm{x}−\mathrm{2}}\right)…
Question Number 193596 by Mingma last updated on 17/Jun/23 Answered by cortano12 last updated on 17/Jun/23 $$\left(\mathrm{1}\right)\:\gamma=\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}} −\mathrm{2}\alpha\mathrm{x}−\beta}{\mathrm{2x}}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\:\:\beta=\mathrm{1}\: \\ $$$$\:\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 193532 by horsebrand11 last updated on 16/Jun/23 $$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}} }\:=? \\ $$ Answered by aba last updated on 16/Jun/23 $$\mathrm{let}\:\mathrm{t}=\mathrm{2}−\mathrm{x} \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}}…
Question Number 193563 by SaRahAli last updated on 16/Jun/23 Answered by Gamil last updated on 16/Jun/23 Answered by Subhi last updated on 16/Jun/23 $$ \\…
Question Number 193540 by LowLevelLump last updated on 16/Jun/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 193408 by cortano12 last updated on 13/Jun/23 $$\:\underline{\underbrace{ }} \\ $$ Answered by MM42 last updated on 13/Jun/23 $${lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{{n}}×\left(\frac{\mathrm{1}−\left({e}^{\frac{{a}}{{n}}} \right)^{{n}} ×\frac{\mathrm{1}}{{e}^{\frac{{a}}{{n}}} }}{\mathrm{1}−{e}^{\frac{{a}}{{n}}}…