Question Number 132153 by Ñï= last updated on 11/Feb/21 Commented by Ar Brandon last updated on 11/Feb/21 No username ?! ���� Answered by Olaf last updated on 11/Feb/21…
Question Number 1083 by Vishal last updated on 08/Jun/15 $${Let}\:{a},{b},{c},{p}\:{be}\:{rational}\:{numbers}\:{such}\:{that}\:{p}\:{is}\:{not}\:{a}\:{perfect}\:{cube}. \\ $$$${If}\:{a}+{bp}^{\frac{\mathrm{1}}{\mathrm{3}}} +{cp}^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{0},\:{then}\:{prove}\:{that}\:{a}={b}={c}=\mathrm{0}. \\ $$ Answered by prakash jain last updated on 08/Jun/15 $${p}^{\mathrm{1}/\mathrm{3}}…
Question Number 66619 by mr W last updated on 17/Aug/19 $${solve}\:{for}\:{x},{y}\in{R} \\ $$$$\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{ln}\:\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}=\frac{\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }}{\mathrm{ln}\:\left({y}+\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }\right)} \\ $$ Answered by Smail last updated on…
Question Number 1077 by Vishal last updated on 07/Jun/15 $${Find}\:{the}\:{smallest}\:{number}\:{which}\:{leaves}\:{remainders}\:\mathrm{8}\:{and}\:\mathrm{12}\: \\ $$$${when}\:{divided}\:{by}\:\mathrm{28}\:{and}\:\mathrm{32}\:{respectively}. \\ $$ Commented by prakash jain last updated on 07/Jun/15 $$\mathrm{I}\:\mathrm{assume}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{smallest}\:+\mathrm{ve}\:\mathrm{integer}. \\ $$…
Question Number 132150 by mohammad17 last updated on 11/Feb/21 $${Solve}:\frac{\mid{x}+\mathrm{2}\mid}{{x}−\mathrm{4}}\leqslant\frac{\mathrm{1}}{\mid{x}\mid} \\ $$ Answered by benjo_mathlover last updated on 11/Feb/21 $$\mathrm{case}\left(\mathrm{1}\right)\:\mathrm{x}>\mathrm{0}\:\Rightarrow\:\frac{\mathrm{x}+\mathrm{2}}{\mathrm{x}−\mathrm{4}}\:−\frac{\mathrm{1}}{\mathrm{x}}\leqslant\mathrm{0} \\ $$$$\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{x}+\mathrm{4}}{\mathrm{x}\left(\mathrm{x}−\mathrm{4}\right)}\leqslant\mathrm{0}\:;\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{4}}{\mathrm{x}\left(\mathrm{x}−\mathrm{4}\right)}\leqslant\mathrm{0} \\…
Question Number 1074 by Yugi last updated on 05/Jun/15 $${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)…