Question Number 1074 by Yugi last updated on 05/Jun/15 $${Prove}\:{by}\:{induction}\:{the}\:{following}\:{result}\:{where}\:{N}\:{is}\:{a}\:{positive}\:{even}\:{integer}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}_{\mathrm{1}} ^{\mathrm{2}} +{S}_{\mathrm{2}} ^{\mathrm{2}} =\mathrm{2}^{{N}} \\ $$$${where}\:\:\:\:{S}_{\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{\frac{{N}}{\mathrm{2}}+\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \begin{pmatrix}{{N}}\\{\mathrm{2}\left({r}−\mathrm{1}\right)}\end{pmatrix}\:\:\:\:{and}\:\:\:\:\:\:{S}_{\mathrm{2}} =\underset{{r}=\mathrm{1}} {\overset{{N}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{{r}+\mathrm{1}}…
Question Number 1073 by sai dinesh last updated on 04/Jun/15 $${what}\:{r}\:{u}\:{studying}?…{please}\:{Answer}\:{me} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1068 by 123456 last updated on 01/Jun/15 $${f}:\mathbb{R}\rightarrow\mathbb{R}_{+} ,{g}:\mathbb{R}\rightarrow\mathbb{R}_{+} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{g}\left({x}+\mathrm{1}\right) \\ $$$$\left[{g}\left({x}\right)\right]^{\mathrm{2}} ={f}\left({x}−\mathrm{1}\right){g}\left({x}+\mathrm{1}\right) \\ $$$${f}\left(−\mathrm{1}\right)=\mathrm{1},{g}\left(\mathrm{1}\right)=\mathrm{2},{f}\left(\mathrm{0}\right){g}\left(\mathrm{0}\right)=? \\ $$ Answered by prakash jain last…
Question Number 132137 by benjo_mathlover last updated on 11/Feb/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{3}} }\left(\mathrm{sin}^{−\mathrm{1}} \mathrm{x}−\mathrm{tan}^{−\mathrm{1}} \mathrm{x}\right)\right)^{\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }} =? \\ $$ Answered by EDWIN88 last updated on 11/Feb/21…
Question Number 66602 by aliesam last updated on 17/Aug/19 Commented by Rio Michael last updated on 17/Aug/19 $$\left.\mathrm{16}\right)\:{let}\:{y}\:=\:{x}^{\mathrm{3}} \\ $$$$\:\:\Rightarrow\:\:\frac{{dy}}{{dx}}\:=\:\mathrm{3}{x}^{\mathrm{2}} \\ $$$$\:\frac{{dy}}{{dx}}\mid_{{x}\:=\:−\mathrm{1}} \:=\:\mathrm{3} \\ $$$${when}\:{x}\:=\:−\mathrm{1}\:\:,\:{y}\:=\:−\mathrm{1}\:\:{hence}\:{pt}\:\:\left(−\mathrm{1},−\mathrm{1}\right)…
Question Number 1067 by Yugi last updated on 30/May/15 $${Let}\: \\ $$$$\:\:\:\:\:\:{S}_{{N}} =\underset{{n}=\mathrm{1}} {\overset{{N}} {\sum}}\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {n}^{\mathrm{3}} \:. \\ $$$${Find}\:{S}_{\mathrm{2}{N}} \:{in}\:{terms}\:{of}\:{N}.\: \\ $$$$ \\ $$ Answered…
Question Number 1066 by 123456 last updated on 27/May/15 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{{x}}{\mathrm{tan}\:{x}}{dx} \\ $$ Answered by malwaan last updated on 01/Jun/15 $$\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$ Terms…
Question Number 132138 by benjo_mathlover last updated on 11/Feb/21 $$\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} }{\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} }\:−\:\mathrm{e}^{\mathrm{2}} \:\right)\mathrm{n}^{\mathrm{2}} =? \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\mathrm{L}=\mathrm{e}^{\mathrm{2}}…
Question Number 66601 by aliesam last updated on 17/Aug/19 Commented by kaivan.ahmadi last updated on 17/Aug/19 $$\mathrm{14} \\ $$$${D}=\left(\mathrm{0},+\infty\right)\Rightarrow{c}\:{is}\:{true} \\ $$ Answered by Rio Michael…
Question Number 1063 by lops55 last updated on 26/May/15 $${rational}\:{number}\:{which}\:{is}\:{neither}\:{negetive}\:{nor}\:{positive} \\ $$ Answered by 123456 last updated on 01/Jun/15 $$\mathrm{0}? \\ $$ Terms of Service…