Question Number 195905 by cortano12 last updated on 13/Aug/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3}+\mathrm{x}^{\mathrm{4}} }\:−\sqrt{\mathrm{3}+\mathrm{tan}\:^{\mathrm{4}} \mathrm{x}}}{\mathrm{x}^{\mathrm{6}} }\:=? \\ $$ Answered by qaz last updated on 13/Aug/23 $$ \\…
Question Number 195840 by NANIGOPAL last updated on 11/Aug/23 $${find}\:{the}\:{valur} \\ $$$$\:\:{li}\underset{\rightarrow\mathrm{0}} {{m}}\:\frac{{x}−{sinx}}{{x}^{\mathrm{3}} } \\ $$ Commented by kokeb last updated on 11/Aug/23 $${find}\:{the}\:{valur} \\…
Question Number 195772 by dimentri last updated on 10/Aug/23 $$\:\:\:\:\cancel{\underline{\underbrace{ }}}\:\cancel{ } \\ $$ Answered by MM42 last updated on 10/Aug/23 $${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}} \:\:\frac{{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}\:−\mathrm{2}{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}×{sin}\frac{\mathrm{3}{x}}{\mathrm{2}}}{\mathrm{4}{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}{sin}\frac{\mathrm{3}{x}}{\mathrm{2}}{cos}\mathrm{3}{x}} \\ $$$$={lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}}…
Question Number 195619 by cortano12 last updated on 06/Aug/23 $$\:\:\:\cancel{\underline{\underbrace{ }}} \\ $$ Answered by MM42 last updated on 06/Aug/23 $$\infty \\ $$ Answered by…
Question Number 195618 by cortano12 last updated on 06/Aug/23 $$\:\:\:\:\cancel{\underline{\underbrace{ }}} \\ $$ Answered by MM42 last updated on 06/Aug/23 $$\mathrm{0} \\ $$ Commented by…
Question Number 195569 by York12 last updated on 05/Aug/23 $${a}_{{i}} ,{b}_{{i}} ,{x}_{{i}} {be}\:{reals}\:{for}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},…,{n},\:{such}\:{that} \\ $$$$\sum_{{i}=\mathrm{1}} ^{{n}} \left[{a}_{{i}} {x}_{{i}} \right]=\mathrm{0}.\:{Prove}\:{that} \\ $$$$\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{x}_{{i}} ^{\mathrm{2}} \right]\right)\left(\underset{{i}=\mathrm{1}}…
Question Number 195401 by mnjuly1970 last updated on 01/Aug/23 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calc}\underset{\underset{\Downarrow} {\Downarrow}} {\mathrm{u}late} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{lim}_{\:\mathrm{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\left(\:\:\mathrm{sin}\left(\mathrm{x}\:\right)\right)^{\:\mathrm{tan}^{\:\mathrm{2}} \left(\mathrm{x}\:\right)} \:\:\:\:=\:?\:\:\:\:\:\:\:\:\begin{array}{|c|c|}\\\\\hline\end{array} \\ $$$$…
Question Number 195395 by cortano12 last updated on 01/Aug/23 Answered by kapoorshah last updated on 01/Aug/23 $${Any}\:{number}\:{power}\:\mathrm{0}\:{is}\:\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{1}\:+\:\infty\:+\:\infty\:+\:…\:+\:\infty\right)^{\mathrm{0}} \:=\:\mathrm{1} \\ $$ Terms…
Question Number 195365 by Mr.D.N. last updated on 31/Jul/23 $$\:\: \\ $$$$\:\underset{\mathrm{x}\rightarrow\mathrm{y}} {\overset{\mathrm{lim}} {\:}}\:\frac{\mathrm{tan}\:\mathrm{x}−\mathrm{tany}}{\mathrm{x}−\mathrm{y}} \\ $$$$ \\ $$ Answered by cortano12 last updated on 31/Jul/23…
Question Number 195325 by mathlove last updated on 30/Jul/23 $${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{{tan}\left(\frac{{x}}{\mathrm{2}}\right)−\mathrm{1}}{{x}−\frac{\pi}{\mathrm{2}}}=\mathrm{1} \\ $$ Answered by BaliramKumar last updated on 30/Jul/23 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\frac{\mathrm{d}}{\mathrm{dx}}\left({tan}\left(\frac{{x}}{\mathrm{2}}\right)−\mathrm{1}\right)}{\frac{\mathrm{d}}{\mathrm{dx}}\left({x}−\frac{\pi}{\mathrm{2}}\right)}\:=\:\frac{\mathrm{sec}^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\centerdot\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}}…