Question Number 37224 by abdo.msup.com last updated on 11/Jun/18 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} \:−\left(\mathrm{1}−{jx}\right)^{{n}} \:{with} \\ $$$${j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{find}\:{p}\:{at}\:\:{form}\:{r}\left({x}\right){e}^{{i}\theta\left({x}\right)} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {r}\left({x}\right)\:{e}^{{i}\theta\left({x}\right)} {dx}\:. \\ $$ Terms of Service…
Question Number 37225 by abdo.msup.com last updated on 11/Jun/18 $${let}\:{n}\geqslant\mathrm{2}\:{and}\:{f}\:\::\:{R}_{{n}} \left[{x}\right]\rightarrow{R}_{\mathrm{2}} \left[{x}\right]\:/ \\ $$$${f}\left({p}\right)\:={xp}\left(\mathrm{1}\right)\:+\left({x}^{\mathrm{2}} \:−\mathrm{4}\right){p}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{linear} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{dim}\:{Kerf}\:{and}\:{dimIm}\left({f}\right) \\ $$ Terms of Service Privacy…
Question Number 37179 by rahul 19 last updated on 10/Jun/18 $$\int\:\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} }\:{dx}\:=\:? \\ $$ Commented by rahul 19 last updated on 10/Jun/18 $$\mathrm{ok}\:\mathrm{sir}.…
Question Number 37171 by behi83417@gmail.com last updated on 10/Jun/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 102698 by bramlex last updated on 10/Jul/20 Answered by bramlex last updated on 10/Jul/20 $$\int\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{h}\left(\mathrm{x}\right)\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{h}'\left(\mathrm{x}\right) \\ $$$$\mathrm{5}+{x}^{\mathrm{2}} {f}\left({x}\right)\:=\:\mathrm{16}{x}^{\mathrm{3}} −\frac{\mathrm{15}}{\mathrm{2}}\sqrt{{x}}\: \\ $$$${x}^{\mathrm{2}} {f}\left({x}\right)=\mathrm{16}{x}^{\mathrm{3}} −\frac{\mathrm{15}\sqrt{{x}}}{\mathrm{2}}−\mathrm{5}…
Question Number 102690 by bramlex last updated on 10/Jul/20 $$\left(\mathrm{1}\right)\int\frac{\mathrm{1}}{\mathrm{cos}\:\sqrt{\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\mathrm{1}}{\mathrm{2}+\mathrm{cot}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\left(\mathrm{3}\right)\:\int\:\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{cos}\:\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 10/Jul/20 $$\left.\mathrm{2}\right)\int\frac{{tanx}}{\mathrm{2}{tanx}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{tanx}+\mathrm{1}}{\mathrm{2}{tanx}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{1}}{\mathrm{2}{tanx}+\mathrm{1}}=\frac{{x}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}}{\left(\mathrm{2}{t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…
Question Number 37143 by rahul 19 last updated on 09/Jun/18 $$\mathrm{Why}\:\mathrm{are}\:\mathrm{following}\:\mathrm{statements}\:\mathrm{wrong}? \\ $$$$\left.\mathrm{a}\right)\:\mathrm{There}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{function}\:\mathrm{with}\:\mathrm{domain}\: \\ $$$$\mathrm{R}\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{x}\right)<\mathrm{0}\:\forall\mathrm{x}\:,\:\mathrm{f}'\left(\mathrm{x}\right)>\mathrm{0}\forall\mathrm{x}\:\mathrm{and} \\ $$$$\mathrm{f}''\left(\mathrm{x}\right)>\mathrm{0}\forall\mathrm{x}. \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{If}\:\mathrm{f}''\left(\mathrm{c}\right)=\mathrm{0}\:\mathrm{then}\:\left(\mathrm{c},\mathrm{f}\left(\mathrm{c}\right)\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{inflection} \\ $$$$\mathrm{point}. \\ $$…
Question Number 168188 by cortano1 last updated on 05/Apr/22 $$\:\:\:\:\:\int\:\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$ Commented by Florian last updated on 09/Apr/22 $$\:\:?=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}{arctan}\left(\sqrt{\mathrm{2}}\:{tan}\left(\mathrm{2}{x}\right)\right)+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{2}}}\left({ln}\mid\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}{cos}\left(\mathrm{2}{x}\right)+\mathrm{1}\mid\:{ln}\mid\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}{cos}\left(\mathrm{2}{x}\right)−\mathrm{1}\mid\right)+{c},\:{c}\in{R} \\ $$ Answered by…
Question Number 37108 by rahul 19 last updated on 09/Jun/18 $$\mathrm{If}\:\mathrm{4}{x}+\mathrm{8cos}\:{x}+\mathrm{tan}\:{x}−\mathrm{2sec}\:{x}−\mathrm{4log}\:\left\{\mathrm{cos}{x}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\right\}\geqslant\mathrm{6} \\ $$$$\forall\:{x}\:\epsilon\:\left[\mathrm{0},\psi\right)\:\mathrm{then}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\psi\:\mathrm{is}\:? \\ $$ Answered by ajfour last updated on 09/Jun/18 $${f}\left({x}\right)=\mathrm{4}{x}+\mathrm{8cos}\:{x}+\mathrm{tan}\:{x}−\mathrm{4ln}\:\left\{\mathrm{cos}\:{x}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\right\}−\mathrm{6} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{8}…
Question Number 37079 by rahul 19 last updated on 08/Jun/18 Answered by ajfour last updated on 09/Jun/18 $${f}\:''\left({x}\right)−\mathrm{3}{f}\:'\left({x}\right)\:>\:\mathrm{3} \\ $$$$\Rightarrow\:\:\:{f}\:''\left(\mathrm{0}\right)\:>\:\mathrm{0} \\ $$$${for}\:{x}\:>\:\mathrm{0}\:\:{f}\:'\left({x}\right)\:>\:−\mathrm{1}\:\:\:\:\:\:\:….\left({i}\right) \\ $$$$\frac{{d}}{{dx}}\left[\:{f}\left({x}\right)+{x}\right]\:=\:{f}\:'\left({x}\right)+\mathrm{1}\: \\…