Question Number 60410 by tanmay last updated on 20/May/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{{x}^{\mathrm{2}} }{{tanxsinx}}\right]\:\left[.\right]={grestest}\:{integer}\:{function} \\ $$ Commented by kaivan.ahmadi last updated on 20/May/19 $${if}\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}} \\ $$$${sinx}<{x}<{tgx}\Rightarrow{xsinx}<{x}^{\mathrm{2}} <{xtgx}\Rightarrow…
Question Number 191483 by Mastermind last updated on 24/Apr/23 $$\mathrm{Compute}\:\mathrm{the}\:\mathrm{min}−\mathrm{max}\:\mathrm{polynomial} \\ $$$$\mathrm{q}_{\mathrm{1}} ^{\ast} \left(\mathrm{x}\right)\:\mathrm{to}\:\mathrm{e}^{\mathrm{x}} \:\mathrm{on}\:\mathrm{interval}\:\left[−\mathrm{1},\:\mathrm{1}\right]. \\ $$$$ \\ $$$$\mathrm{Anyone}?? \\ $$ Terms of Service Privacy…
Question Number 125939 by Dwaipayan Shikari last updated on 15/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{cos}\mathrm{2}{x}−{tanx}.{cot}\left({tanx}\right)}{{sin}\mathrm{2}{x}−{tan}\left({tanx}\right){log}\left({cos}^{\mathrm{2}} {x}\right)}{dx} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125884 by Dwaipayan Shikari last updated on 14/Dec/20 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{5}}−\mathrm{2}\right)^{{n}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}{\left(\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\left(\sqrt{\mathrm{5}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\right)^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} +\left(\sqrt{\mathrm{5}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\right)^{{n}−\frac{\mathrm{1}}{\mathrm{2}}} \right)\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60337 by arcana last updated on 20/May/19 $$\mathrm{15},\mathrm{25},\mathrm{42},…? \\ $$ Commented by MJS last updated on 20/May/19 $$\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\infty\:\mathrm{solutions}: \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}−{y}=\mathrm{0} \\ $$$${a}+{b}+{c}−\mathrm{15}=\mathrm{0}…
Question Number 125857 by Dwaipayan Shikari last updated on 14/Dec/20 $$\mathrm{1}+\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{7}} +\mathrm{7}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}.\mathrm{4}}\right)^{\mathrm{7}} +\mathrm{10}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}.\mathrm{4}.\mathrm{6}}\right)^{\mathrm{7}} +… \\ $$ Answered by Olaf last updated on 14/Dec/20 $$\mathrm{S}\:=\:\mathrm{1}+\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 60308 by Tawa1 last updated on 19/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60307 by Tawa1 last updated on 19/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60256 by rahul 19 last updated on 19/May/19 Answered by mr W last updated on 19/May/19 $$\mathrm{2}{x}+\mathrm{4}{y}=\mathrm{2}\left({x}+{y}\right)+\mathrm{2}{y}\leqslant\mathrm{8}+\mathrm{2}{y} \\ $$$$\leqslant\mathrm{8}+\mathrm{2}\left(\mathrm{4}−{x}\right)=\mathrm{16}−\mathrm{2}{x}\leqslant\mathrm{16}\:! \\ $$$$ \\ $$$${z}=\mathrm{2}{x}+\mathrm{5}{y}=\mathrm{2}\left({x}+{y}\right)+\mathrm{3}{y}\leqslant\mathrm{8}+\mathrm{3}{y}…
Question Number 60257 by rahul 19 last updated on 19/May/19 $${The}\:{maximum}\:{value}\:{of}\:{Z}=\mathrm{4}{x}+\mathrm{2}{y} \\ $$$${subject}\:{to}\:{constraints}\:\mathrm{2}{x}+\mathrm{3}{y}\leqslant\mathrm{18}\:, \\ $$$${x}+{y}\geqslant\mathrm{10}\:{and}\:{x},{y}\geqslant\mathrm{0}\:{is}\:? \\ $$ Commented by rahul 19 last updated on 19/May/19…