Question Number 193967 by Risandu last updated on 24/Jun/23 Answered by MM42 last updated on 24/Jun/23 $${lim}_{\theta\rightarrow\pi} \:\:\frac{\mathrm{4}{sin}\theta{cos}\theta\left({cos}\theta−{sin}\mathrm{3}\theta\right)}{\left(\pi−\theta\right)\left(\pi+\theta\right)} \\ $$$${let}\:\:\:\:\theta=\pi−{u} \\ $$$$\Rightarrow{lim}_{{u}\rightarrow\mathrm{0}} \:\frac{−\mathrm{4}{sinu}×{cosu}×\left({sin}\mathrm{3}{u}−{cosu}\right)}{{u}×\left(\mathrm{2}\pi−{u}\right)} \\ $$$$\:=\frac{\mathrm{2}}{\pi}\:\checkmark…
Question Number 193960 by pete last updated on 25/Jun/23 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin}^{\mathrm{7}} \theta\:=\frac{\mathrm{1}}{\mathrm{64}}\left(\mathrm{35sin}\theta\:−\mathrm{21sin3}\theta\right. \\ $$$$+\mathrm{7sin5}\theta−\mathrm{sin7}\theta\:\:\mathrm{using} \\ $$$$\:\mathrm{1}.\:\mathrm{sin}\theta\:=\frac{\mathrm{e}^{\mathrm{i}\theta} −\mathrm{e}^{−\mathrm{i}\theta} }{\mathrm{2i}}\:\mathrm{and}\: \\ $$$$\mathrm{2}.\:\left(\mathrm{cos}\theta+\mathrm{isin}\theta\right)^{\mathrm{n}} \:=\:\mathrm{cos}\:\mathrm{n}\theta+\mathrm{sin}\:\mathrm{n}\theta \\ $$$$ \\ $$ Terms…
Question Number 193962 by Abdullahrussell last updated on 24/Jun/23 Answered by AST last updated on 24/Jun/23 $$\Rightarrow{f}\left({x}\right)={Q}\left({x}\right)\left({x}−{a}\right)\left({x}−{b}\right)+{R}\Rightarrow{f}\left({a}\right)={R},{f}\left({b}\right)={R} \\ $$$$\Rightarrow\frac{{f}\left({a}\right)\left({x}−{b}\right)−{f}\left({b}\right)\left({x}−{a}\right)}{{a}−{b}}=\frac{{R}\left({x}−{b}−{x}+{a}\right)}{{a}−{b}}={R} \\ $$ Answered by cortano12 last…
Question Number 193972 by Rupesh123 last updated on 24/Jun/23 Commented by Frix last updated on 25/Jun/23 $$\mathrm{Ok}\:\mathrm{I}\:\mathrm{thought}\:\mathrm{about}\:\mathrm{it}.\:\mathrm{What}\:\mathrm{now}? \\ $$ Commented by Rupesh123 last updated on…
Question Number 193975 by mr W last updated on 24/Jun/23 Commented by mr W last updated on 25/Jun/23 $${find}\:{the}\:{area}\:{of}\:{the}\:{hatched}\:{square}. \\ $$ Answered by mr W…
Question Number 193958 by Rupesh123 last updated on 24/Jun/23 Answered by ARUNG_Brandon_MBU last updated on 24/Jun/23 $$\frac{{a}}{\mathrm{sin}\left(\mathrm{150}°−{x}\right)}=\frac{{b}}{\mathrm{sin30}°}=\mathrm{2}{b} \\ $$$$\frac{{a}}{\mathrm{sin30}°}=\frac{{a}+{b}}{\mathrm{sin}\left(\mathrm{150}°−{x}\right)}=\mathrm{2}{a} \\ $$$$\Rightarrow\mathrm{2}{b}\left({a}+{b}\right)=\mathrm{2}{a}^{\mathrm{2}} \:\Rightarrow{a}^{\mathrm{2}} −{ab}−{b}^{\mathrm{2}} =\mathrm{0} \\…
Question Number 193971 by mnjuly1970 last updated on 24/Jun/23 $$ \\ $$$$\:\:\:\:\:\:{y}=\:\lfloor\:{x}^{\:\mathrm{2}} \:\rfloor\:+\:\lfloor\:{x}\:\rfloor\:\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:{R}_{{y}} \:=?\:\:\:\:\:\:\:{Range} \\ $$ Answered by MM42 last updated…
Question Number 193949 by sonukgindia last updated on 23/Jun/23 Answered by aleks041103 last updated on 23/Jun/23 $$\mathrm{8}^{{x}} −\mathrm{8}{x}={f}\left({x}\right) \\ $$$${f}\:'\left({x}\right)={ln}\left(\mathrm{8}\right)\mathrm{8}^{{x}} −\mathrm{8};\:{f}\:'\left({x}_{\mathrm{0}} \right)=\mathrm{0} \\ $$$${f}\:''\left({x}\right)={ln}\left(\mathrm{8}\right)^{\mathrm{2}} \mathrm{8}^{{x}}…
Question Number 193951 by Erico last updated on 23/Jun/23 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}!}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} {t}^{{n}} {e}^{−{t}} {dt}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by senestro last updated on…
Question Number 193918 by Rupesh123 last updated on 23/Jun/23 Terms of Service Privacy Policy Contact: info@tinkutara.com