Question Number 131295 by EDWIN88 last updated on 03/Feb/21 $${Find}\:{domain}\:{of}\:{function}\: \\ $$$${f}\left({x}\right)=\:\sqrt{\frac{\mathrm{cos}\:{x}−\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{6}+\mathrm{35}{x}−\mathrm{6}{x}^{\mathrm{2}} }}\: \\ $$ Answered by liberty last updated on 03/Feb/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{1}/\mathrm{2}}{\mathrm{6}+\mathrm{35x}−\mathrm{6x}^{\mathrm{2}} }}\: \\…
Question Number 221 by 123456 last updated on 25/Jan/15 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\…
Question Number 131288 by mohammad17 last updated on 03/Feb/21 Answered by liberty last updated on 11/Feb/21 $$\mathrm{L}=\int\:\sqrt{\frac{\mathrm{1}−\mathrm{3x}^{−\mathrm{3}} }{\mathrm{x}^{\mathrm{8}} }}\:\mathrm{dx}\:=\:\int\:\mathrm{x}^{−\mathrm{4}} \:\sqrt{\mathrm{1}−\mathrm{3x}^{−\mathrm{3}} }\:\mathrm{dx} \\ $$$$\mathrm{change}\:\mathrm{of}\:\mathrm{variable}\::\:\sqrt{\mathrm{1}−\mathrm{3x}^{−\mathrm{3}} }\:=\:\mathrm{h}\:\mathrm{or}\:\mathrm{1}−\mathrm{3x}^{−\mathrm{3}} =\mathrm{h}^{\mathrm{2}}…
Question Number 131291 by mohammad17 last updated on 03/Feb/21 $${is}\:{the}\:{sequence}\:\langle{an}\rangle=\langle\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}}\rangle\:{converge} \\ $$$${or}\:{diverge}\:{and}\:{bounded}\:{or}\:{not}\:{bounded}\:? \\ $$ Commented by mohammad17 last updated on 03/Feb/21 $${how}\:{can}\:{solve}\:{this} \\ $$…
Question Number 65753 by Masumsiddiqui399@gmail.com last updated on 03/Aug/19 Answered by mr W last updated on 04/Aug/19 $$\mathrm{1}\:\:\:^{\left.\ast\right)} \\ $$$$\sqrt{\mathrm{1}+\mathrm{1}} \\ $$$$\sqrt{\sqrt{\mathrm{1}+\mathrm{1}}+\mathrm{1}} \\ $$$$\sqrt{\sqrt{\sqrt{\mathrm{1}+\mathrm{1}}+\mathrm{1}}+\mathrm{1}} \\…
Question Number 216 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate} \\ $$$$\underset{−\infty} {\overset{+\infty} {\int}}{f}\left({x}\right){dx} \\ $$$$\mathrm{where} \\ $$$${f}\left({x}\right)=\begin{cases}{{e}^{{x}} }&{{x}\leqslant\mathrm{0}}\\{\mathrm{1}+{x}}&{\mathrm{0}<{x}\leqslant\mathrm{1}}\\{\mathrm{1}+{x}^{\mathrm{2}} }&{\mathrm{1}<{x}\leqslant\mathrm{2}}\\{\mathrm{5}}&{\mathrm{2}<{x}\leqslant\mathrm{5}}\\{\frac{\mathrm{5}}{\mathrm{1}+\left({x}−\mathrm{5}\right)^{\mathrm{2}} }}&{{x}>\mathrm{5}}\end{cases} \\ $$ Answered by…
Question Number 131285 by EDWIN88 last updated on 03/Feb/21 $${How}\:{many}\:{curves}\:{with}\:{equation} \\ $$$${Ax}^{\mathrm{2}} −\left(\frac{{B}}{\mathrm{2}}{y}\right)^{\mathrm{2}} =\:\mathrm{0}\:{with}\:{A}\:{and}\:{B}\:{two} \\ $$$${different}\:{numbers}\:{are}\:{selected}\: \\ $$$${from}\:{the}\:{set}\:\left\{\:−\mathrm{3},−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{3}\:\right\}\:? \\ $$$$\left({a}\right)\:\mathrm{8}\:\:\:\:\:\:\left({b}\right)\mathrm{10}\:\:\:\:\:\left({c}\right)\mathrm{12} \\ $$$$\left({d}\right)\:\mathrm{22}\:\:\:\left({e}\right)\:\mathrm{20} \\ $$ Answered…
Question Number 215 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate} \\ $$$$\mathrm{1}+\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{4}^{\mathrm{5}} } \left(\mathrm{mod}\:\mathrm{10}\right) \\ $$ Answered by prakash jain last updated on 16/Dec/14…
Question Number 131286 by mnjuly1970 last updated on 03/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:{find}\:::\:\:{i}::\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{4}} −\mathrm{1}}\right)=? \\ $$$$\:\:\:\: \\…
Question Number 65749 by bshahid010@gmail.com last updated on 03/Aug/19 Answered by Tanmay chaudhury last updated on 03/Aug/19 $${sin}^{\mathrm{2}} {x}+{sin}^{\mathrm{4}} {x}+{sin}^{\mathrm{6}} {x}+…\infty \\ $$$$=\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}−{sin}^{\mathrm{2}} {x}}…