Question Number 219868 by Nicholas666 last updated on 02/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}; \\ $$$$\:\:\:\:\frac{{d}}{{dx}}\:\left(\frac{\mathrm{sin}^{\:\mathrm{2}} {x}}{\mathrm{1}+\mathrm{cot}\:{x}}\:+\:\frac{\mathrm{cos}^{\:\mathrm{2}} {x}}{\mathrm{1}+\mathrm{tan}\:{x}}\right)\:=\:−\mathrm{cos}\:\mathrm{2}{x}\:\:\:\: \\ $$$$ \\ $$ Answered by MrGaster last updated…
Question Number 219451 by Nicholas666 last updated on 25/Apr/25 Commented by Nicholas666 last updated on 25/Apr/25 $$\mathrm{This}\:\mathrm{is}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{beyond}\:\mathrm{My}\:\mathrm{control},\:\:\: \\ $$$$\:\mathrm{can}\:\mathrm{You}\:\mathrm{solve}\:\mathrm{friends}? \\ $$$$ \\ $$ Terms of…
Question Number 219243 by mnjuly1970 last updated on 21/Apr/25 Commented by mr W last updated on 23/Apr/25 $${i}\:{got}\:\left({solution}\:{see}\:{below}\right) \\ $$$${y}={C}_{\mathrm{1}} \mathrm{sin}\:\left(\mathrm{tan}^{−\mathrm{1}} {x}+{C}_{\mathrm{2}} \right) \\ $$…
Question Number 219098 by zetamaths last updated on 20/Apr/25 $$\zeta\left(\alpha\right)=\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\alpha} }\:\: \\ $$ Answered by Frix last updated on 20/Apr/25 $$\mathrm{This}\:\mathrm{is}\:\mathrm{just}\:\mathrm{the}\:\mathrm{definition}\:\mathrm{of}\:\mathrm{the}\:\zeta−\mathrm{Function}, \\ $$$$\mathrm{there}'\mathrm{s}\:\mathrm{nothing}\:\mathrm{to}\:\mathrm{solve}.…
Question Number 216800 by depressiveshrek last updated on 21/Feb/25 Answered by MrGaster last updated on 21/Feb/25 $$\mathrm{Prove}:{f}\left({x}\right)={a}\left({x}−{r}_{\mathrm{1}} \right)^{{m}_{\mathrm{1}} } \left({x}−{r}_{\mathrm{2}} \right)^{{m}_{\mathrm{2}} } \ldots\left({x}−{r}_{{k}} \right)^{{m}_{{k}} }…
Question Number 216694 by sniper237 last updated on 16/Feb/25 $${Prove}\:{that}\:\:^{\mathrm{3}} \sqrt{\sqrt{\mathrm{5}}+\mathrm{2}}\:−^{\mathrm{3}} \sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}\:=\mathrm{1} \\ $$ Answered by golsendro last updated on 16/Feb/25 $$\:\mathrm{let}\:\mathrm{x}=\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}+\mathrm{2}}−\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}−\mathrm{2}} \\ $$$$\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}+\mathrm{2}}−\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}−\mathrm{2}}−\mathrm{x}\:=\:\mathrm{0}\: \\…
Question Number 216638 by Nadirhashim last updated on 13/Feb/25 $$\:\:\boldsymbol{{without}}\:\boldsymbol{{using}}\:\boldsymbol{{LHopital}} \\ $$$$\:\:\:\boldsymbol{{rule}}\:\boldsymbol{{evalute}}\: \\ $$$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\boldsymbol{{ln}}\left(\mathrm{1}−{x}\right)−\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\:}{\mathrm{1}−\boldsymbol{{cox}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)} \\ $$ Commented by MathematicalUser2357 last updated on 13/Feb/25…
Question Number 216411 by MathematicalUser2357 last updated on 07/Feb/25 $$\frac{{dx}}{{dx}} \\ $$ Answered by MATHEMATICSAM last updated on 07/Feb/25 $$\mathrm{1} \\ $$ Terms of Service…
Question Number 215979 by alcohol last updated on 23/Jan/25 $${u}_{{n}} \:=\:\underset{{k}={n}+\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:{and}\:{v}_{{n}} \:=\:\underset{{k}={n}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:{and}\:{v}_{{n}} \:{are}\:{adjacent} \\ $$$${use}\:{ln}\left({x}+\mathrm{1}\right)\:\leqslant\:{x}\:{and}\:{x}\leqslant−{ln}\left(\mathrm{1}−{x}\right)\:{and} \\ $$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:\leqslant\:\underset{{k}={n}+\mathrm{1}}…
Question Number 215971 by jigar last updated on 23/Jan/25 $$\frac{}{} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com