Question Number 135986 by SOMEDAVONG last updated on 17/Mar/21 $$\mathrm{I}=\int\mathrm{e}^{\mathrm{sinx}} \left(\frac{\mathrm{xcos}^{\mathrm{2}} \mathrm{x}−\mathrm{sinx}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\right)\mathrm{dx} \\ $$ Answered by Olaf last updated on 17/Mar/21 $$\mathrm{I}\:=\:\int{xe}^{\mathrm{sin}{x}} {dx}−\int{e}^{\mathrm{sin}{x}} \left(\frac{\mathrm{sin}{x}}{\mathrm{cos}^{\mathrm{2}}…
Question Number 70446 by oyemi kemewari last updated on 04/Oct/19 Commented by oyemi kemewari last updated on 04/Oct/19 please help me solve this question Commented by mathmax by abdo last…
Question Number 4911 by FilupSmith last updated on 21/Mar/16 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\emptyset^{{n}} −\lfloor\phi^{{n}} \rfloor\right)=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Where}:\:\:\:\:\:\:\:\phi\:=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lfloor{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{function} \\ $$ Commented by…
Question Number 135976 by I want to learn more last updated on 17/Mar/21 Answered by mr W last updated on 17/Mar/21 $$\frac{{x}}{\mathrm{sin}\:\mathrm{90}°}=\frac{\mathrm{2}}{\mathrm{sin}\:\angle{ADC}}\:\:\:\:…\left({i}\right) \\ $$$$\frac{\mathrm{sin}\:\mathrm{30}°}{\mathrm{3}}=\frac{\mathrm{sin}\:\angle{BDC}}{{y}}\:\:\:…\left({ii}\right) \\…
Question Number 4905 by 123456 last updated on 20/Mar/16 $${f}\left({x}\right)=\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{even}\:\mathrm{function}\:\mathrm{or}\:\mathrm{a}\:\mathrm{odd}\:\mathrm{function}? \\ $$ Commented by Yozzii last updated on 20/Mar/16 $${This}\:{is}\:{indeterminate}\:{I}\:{think}\:{since}\:{f}\left({x}\right)=\mathrm{0} \\ $$$${satisfies}\:{both}\:{f}\left({x}\right)=−{f}\left({x}\right)=\mathrm{0} \\ $$$${and}\:{f}\left(−{x}\right)=\mathrm{0}={f}\left({x}\right). \\…
Question Number 4904 by love math last updated on 20/Mar/16 $${Determine}\:{the}\:{smallest}\:{natural} \\ $$$${value}\:{of}\:{n},\:{so}\:{the}\:{function}\: \\ $$$${y}=\:\mathrm{5}{x}\:{sin}\:\mathrm{5}{nx}\:{will}\:{be}\:{even}. \\ $$ Commented by Yozzii last updated on 20/Mar/16 $${y}\left(−{x}\right)=\mathrm{5}\left(−{x}\right){sin}\left(−\mathrm{5}{nx}\right)…
Question Number 135974 by liberty last updated on 17/Mar/21 $$ \\ $$How do you solve for 2cos^3(x) + sinx – 3sin^2 (x) cos(x) =0? Commented…
Question Number 4900 by prakash jain last updated on 19/Mar/16 $$\int_{{n}} ^{\:{n}+\mathrm{1}} {f}\left({x}\right)\mathrm{d}{x},\:{n}\in\mathbb{N} \\ $$$${where}\:{f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}+\mathrm{1}} {\prod}}\left({x}−{i}\right) \\ $$$$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{integrated}\:\mathrm{with}\:\mathrm{evaluating}\:\mathrm{the} \\ $$$$\mathrm{product}? \\ $$ Commented by…
Question Number 135971 by Raxreedoroid last updated on 17/Mar/21 $$ \\ $$$$\mathrm{Let}\:{R}\left({n},{m}\right)={R}\left({n}−\mathrm{1},{m}\right)+{R}\left({n}−\mathrm{1},{m}−\mathrm{1}\right) \\ $$$$\mathrm{if}\:{R}\left(\mathrm{1},\mathrm{1}\right)=−\mathrm{6},{R}\left(\mathrm{2},\mathrm{1}\right)=\mathrm{8},{R}\left(\mathrm{3},\mathrm{1}\right)=−\mathrm{1} \\ $$$$\mathrm{and}\:\forall{t}\:{R}\left(\mathrm{4},{t}\right)=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\left.{a}\right)\:\mathrm{Find}\:{R}\left(\mathrm{1},\mathrm{21}\right) \\ $$$$ \\…
Question Number 4897 by 123456 last updated on 19/Mar/16 $${f}\left({x}\right)=\mathrm{10sin}\:{x} \\ $$$${g}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{1} \\ $$$${h}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1} \\ $$$${h}\left({g}\left({f}\left({x}\right)\right)\right)=\mathrm{0} \\ $$$${x}=??? \\ $$ Commented by prakash…