Question Number 195148 by horsebrand11 last updated on 25/Jul/23 $$\:\:\begin{array}{|c|}{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{x}\:\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}=?}\\\hline\end{array} \\ $$ Answered by Erico last updated on 25/Jul/23 $$\frac{\mathrm{1}+\mathrm{xsinx}−\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}=\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{x}}{\mathrm{sinx}} \\…
Question Number 195118 by York12 last updated on 25/Jul/23 $${a},{b},{c}>\mathrm{0}\:\&\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{{a}}{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }+\frac{{b}}{{a}^{\mathrm{2}} +{c}^{\mathrm{2}} }+\frac{{c}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\geqslant\frac{\mathrm{3}}{\mathrm{2}}\left(\frac{{a}+{b}+{c}}{{ab}+{bc}+{ac}}\right)^{\mathrm{2}} \\ $$ Commented by York12…
Question Number 195175 by valdirmd last updated on 25/Jul/23 Answered by Rasheed.Sindhi last updated on 26/Jul/23 $${x}^{\mathrm{4}} +{x}^{\mathrm{2}} =\mathrm{11}/\mathrm{5}\:,\:\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{\mathrm{1}/\mathrm{3}} =? \\ $$$$\blacktriangleright{Let}\:{y}=\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{\mathrm{1}/\mathrm{3}} \\…
Question Number 195137 by mathlove last updated on 25/Jul/23 $${f}\left({x}\right)={arctan}\left(\frac{\mathrm{4}{sinx}}{\mathrm{3}+\mathrm{5}{cosx}}\right)\:\:\:{then}\:{f}^{'} \left(\frac{\pi}{\mathrm{3}}\right)=? \\ $$ Answered by Tokugami last updated on 02/Sep/23 $${f}'\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{4sin}\:{x}}{\mathrm{3}+\mathrm{5cos}\:{x}}\right)^{\mathrm{2}} }\:\frac{{d}}{{dx}}\left(\frac{\mathrm{4sin}\:{x}}{\mathrm{3}+\mathrm{5cos}\:{x}}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{16sin}^{\mathrm{2}} {x}}{\left(\mathrm{3}+\mathrm{5cos}\:{x}\right)^{\mathrm{2}}…
Question Number 195136 by mathlove last updated on 25/Jul/23 $${f}\left({x}\right)={arctan}\left({sinx}\right) \\ $$$${and}\:\:{cosa}=\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\:\:\:{faind}\:\:\:{f}^{'} \left({a}\right)=? \\ $$ Answered by som(math1967) last updated on 25/Jul/23 $$\:\boldsymbol{{f}}\:'\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}}×\boldsymbol{{cosx}} \\…
Question Number 195171 by azirali0198316 last updated on 25/Jul/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 195170 by mathlove last updated on 25/Jul/23 $${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{7}} +\mathrm{2}{x}+\mathrm{1}\:\:\:\:\:\:\:;{x}\geqslant\mathrm{2}}\\{{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{4}\:\:\:\:\:\:\:\:;{x}<\mathrm{1}}\end{cases} \\ $$$${f}^{'} \left(\mathrm{1}\right)=? \\ $$ Answered by MM42 last updated on 25/Jul/23 $${f}\left(\mathrm{1}\right)\:,\:{not}\:{available}\:{so}…
Question Number 195101 by mathlove last updated on 24/Jul/23 $$\sqrt{{ln}\mathrm{2}}\:\:\overset{?} {>}{ln}\mathrm{2} \\ $$ Answered by Frix last updated on 24/Jul/23 $$\mathrm{e}^{{x}} =\mathrm{2} \\ $$$$\mathrm{e}>\mathrm{2}\:\Rightarrow\:{x}<\mathrm{1} \\…
Question Number 195116 by SajaRashki last updated on 24/Jul/23 $${hi}.\:{please}\:{represntation}\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:{on}\:{number}'{s}\:{axis} \\ $$$${with}\:{ruler}\:{and}\:{compass}\:{and}\:{pen}. \\ $$$${thank}\:{you} \\ $$ Commented by Frix last updated on 25/Jul/23 $$\mathrm{Impossible}. \\…
Question Number 195113 by SirMUTUKU last updated on 24/Jul/23 Terms of Service Privacy Policy Contact: info@tinkutara.com