Menu Close

Author: Tinku Tara

Question-24555

Question Number 24555 by ajfour last updated on 20/Nov/17 Commented by ajfour last updated on 20/Nov/17 $${Find}\:{the}\:{maximum}\:{radius}\:{of} \\ $$$${a}\:{circle}\:{such}\:{that}\:{it}\:{touches}\:{the} \\ $$$${parabola}\:{y}={Ax}^{\mathrm{2}} \:{at}\:{its}\:{vertex}, \\ $$$${and}\:{lies}\:{above}\:{it}\:{and}\:{cuts}\:{it} \\…

Show-that-tan-1-p-p-2q-tan-1-p-p-q-pi-2-

Question Number 24554 by tawa tawa last updated on 20/Nov/17 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{p}}{\mathrm{p}\:+\:\mathrm{2q}}\right)\:+\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{p}}{\mathrm{p}\:+\:\mathrm{q}}\right)\:=\:\frac{\pi}{\mathrm{2}} \\ $$ Commented by mrW1 last updated on 21/Nov/17 $${that}'{s}\:{not}\:{true}! \\ $$$${let}'{s}\:{say}\:{p}={q}=\mathrm{1}…

Question-155621

Question Number 155621 by mathdanisur last updated on 02/Oct/21 Answered by ghimisi last updated on 03/Oct/21 $$\frac{{a}+{b}+{c}}{\mathrm{6}}=\mathrm{1}\Rightarrow \\ $$$$\left(\frac{{a}+{d}}{{a}}\right)^{\frac{{a}}{\mathrm{6}}} \left(\frac{{b}+{e}}{{b}}\right)^{\frac{{b}}{\mathrm{6}}} \left(\frac{{c}+{f}}{{c}}\right)^{\frac{{c}}{\mathrm{6}}} \leqslant\frac{{a}}{\mathrm{6}}\centerdot\frac{{a}+{d}}{{a}}+\frac{{b}}{\mathrm{6}}\centerdot\frac{{b}+{e}}{{b}}+\frac{{c}}{\mathrm{6}}\centerdot\frac{{c}+{f}}{{c}}=\mathrm{2}\Rightarrow \\ $$$$\left(\frac{{a}+{d}}{{a}}\right)^{{a}} \left(\frac{{b}+{c}}{{b}}\right)^{{b}}…

Find-lim-x-1-x-1-e-x-e-cos-t-5-dt-3-x-3-

Question Number 155620 by mathdanisur last updated on 02/Oct/21 $$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\underset{\boldsymbol{\mathrm{x}}-\mathrm{1}} {\overset{\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} -\boldsymbol{\mathrm{e}}} {\int}}\mathrm{cos}\left(\mathrm{t}^{\mathrm{5}} \right)\mathrm{dt}}{\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{3}}\:=\:? \\ $$ Answered by mindispower last updated on 04/Oct/21…

prove-that-n-1-r-n-n-r-2-2-r-n-1-r-2-n-2-where-r-2k-k-N-

Question Number 24548 by Physics lover last updated on 20/Nov/17 $${prove}\:{that}\: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{r}} {\sum}}\left\{{n}\left({n}−\frac{{r}}{\mathrm{2}}\right)^{\mathrm{2}} \right\}=\:{r}\centerdot\underset{{n}=\mathrm{1}} {\overset{{r}/\mathrm{2}} {\sum}}{n}^{\mathrm{2}} \\ $$$$\:{where}\:\:\:{r}\:=\:\mathrm{2}{k}\:;\:{k}\:\in\:\mathbb{N} \\ $$ Answered by jota…