Question Number 20068 by mondodotto@gmail.com last updated on 21/Aug/17 Commented by mondodotto@gmail.com last updated on 21/Aug/17 $$\mathrm{Help}\:\mathrm{please}! \\ $$ Answered by Tinkutara last updated on…
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Question Number 20044 by mondodotto@gmail.com last updated on 20/Aug/17 Answered by $@ty@m last updated on 20/Aug/17 $$=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{2}{sin}\mathrm{4}{xcos}\mathrm{2}{xdx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\left({sin}\mathrm{6}{x}+{sin}\mathrm{2}{x}\right){dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{sin}\mathrm{6}{xdx}+\frac{\mathrm{1}}{\mathrm{2}}\int{sin}\mathrm{2}{xdx} \\ $$$$=\frac{−{cos}\mathrm{6}{x}}{\mathrm{12}}−\frac{{cos}\mathrm{2}{x}}{\mathrm{4}}+{C} \\ $$…
Question Number 20036 by mondodotto@gmail.com last updated on 20/Aug/17 Answered by sma3l2996 last updated on 21/Aug/17 $$\mathrm{2}{sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{6}}\right)=\frac{\pi}{\mathrm{2}}−{sin}^{−\mathrm{1}} \left(\mathrm{4}{x}\right)\Leftrightarrow{sin}\left(\mathrm{2}{sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{6}}\right)\right)={sin}\left(\frac{\pi}{\mathrm{2}}−{sin}^{−\mathrm{1}} \left(\mathrm{4}{x}\right)\right) \\ $$$$\mathrm{2}{sin}\left({sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{6}}\right)\right){cos}\left({sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{6}}\right)\right)={cos}\left({sin}^{−\mathrm{1}}…
Question Number 20031 by mondodotto@gmail.com last updated on 20/Aug/17 Answered by Tinkutara last updated on 20/Aug/17 $$\underset{\mathrm{1}} {\overset{{n}} {\int}}\left({x}^{\mathrm{2}} \:+\:\mathrm{3}{x}\right){dx}\:=\:\left[\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\:+\:\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}}\right]_{\mathrm{1}} ^{{n}} \\ $$$$=\:\frac{{n}^{\mathrm{3}}…
Question Number 151097 by naka3546 last updated on 18/Aug/21 $${Find}\:\:{sum}\:\:{of}\:\:{this}\:\:{expression}\:. \\ $$$$\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\:+\:\mathrm{2}\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\:+\:\mathrm{3}\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\:+\:\mathrm{4}\begin{pmatrix}{{n}}\\{\mathrm{4}}\end{pmatrix}\:+\:\ldots\:+\:{n}\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix} \\ $$$${Please}\:\:{show}\:\:{your}\:\:{workings}.\:{Thank}\:\:{you}\:. \\ $$ Answered by Olaf_Thorendsen last updated on 18/Aug/21 $$\mathrm{S}_{{n}} \:=\:\underset{{k}=\mathrm{1}}…
Question Number 85557 by naka3546 last updated on 23/Mar/20 $${x}\:\:=\:\:\sqrt{\mathrm{1}+\:\sqrt{\mathrm{5}+\:\sqrt{\mathrm{11}+\:\sqrt{\mathrm{19}+…}}}} \\ $$$${x}\:\:=\:\:\:? \\ $$ Commented by MJS last updated on 23/Mar/20 $$\mathrm{2}? \\ $$ Commented…
Question Number 85540 by M±th+et£s last updated on 22/Mar/20 $${find}\:{the}\:{range} \\ $$$${y}=\frac{{x}+\left[{x}\right]}{\mathrm{1}−\left[{x}\right]+{x}} \\ $$ Answered by mr W last updated on 23/Mar/20 $${for}\:{x}\geqslant\mathrm{0}: \\ $$$${let}\:{x}={n}+{d}\:{with}\:\mathrm{0}\leqslant{d}<\mathrm{1}…
Question Number 151074 by sarahg1186 last updated on 18/Aug/21 $$\mathrm{5}+\mathrm{5}+\mathrm{5} \\ $$ Answered by sarahg1186 last updated on 18/Aug/21 $$\mathrm{15} \\ $$ Terms of Service…
Question Number 85534 by liki last updated on 22/Mar/20 Commented by liki last updated on 22/Mar/20 $$….{please}\:{help}\:{idea}\:{question}\:{no}\:\mathrm{14}\left({a}\right) \\ $$ Commented by liki last updated on…