Question Number 70780 by MJS last updated on 08/Oct/19 $$\frac{\mathrm{1}}{{t}+\sqrt{{u}}+\sqrt{{v}}}= \\ $$$$=\frac{\left({t}−\sqrt{{u}}+\sqrt{{v}}\right)\left({t}+\sqrt{{u}}−\sqrt{{v}}\right)\left({t}−\sqrt{{u}}−\sqrt{{v}}\right)}{\left({t}+\sqrt{{u}}+\sqrt{{v}}\right)\left({t}−\sqrt{{u}}+\sqrt{{v}}\right)\left({t}+\sqrt{{u}}−\sqrt{{v}}\right)\left({t}−\sqrt{{u}}−\sqrt{{v}}\right)}= \\ $$$$=\frac{{t}^{\mathrm{3}} −\left(\sqrt{{u}}+\sqrt{{v}}\right){t}^{\mathrm{2}} −\left(\sqrt{{u}}−\sqrt{{v}}\right)^{\mathrm{2}} {t}+\left({u}−{v}\right)\left(\sqrt{{u}}−\sqrt{{v}}\right)}{{t}^{\mathrm{4}} −\mathrm{2}\left({u}+{v}\right){t}^{\mathrm{2}} +\left({u}−{v}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\frac{\mathrm{1}}{{t}+\sqrt[{\mathrm{3}}]{{u}}+\sqrt[{\mathrm{3}}]{{v}}}= \\…
Question Number 136313 by aurpeyz last updated on 20/Mar/21 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{dx} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{\mathrm{1}−\mathrm{9}{x}^{−\mathrm{2}} }}\:=\:\int\:\frac{{x}^{−\mathrm{3}} }{\:\sqrt{\mathrm{1}−\mathrm{9}{x}^{−\mathrm{2}}…
Question Number 5237 by sanusihammed last updated on 02/May/16 $${find}\:{the}\:{domain}\:{and}\:{range}\:{of}\: \\ $$$${y}\:=\:\left[_{\:\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:<\mathrm{2}} ^{\:\mathrm{3}{x}−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:\geqslant\:\mathrm{2}} \right. \\ $$ Answered by FilupSmith last updated on 02/May/16 $${Domain}\:=\:\left\{{x}:\:−\infty\leqslant{x}\leqslant\infty\right\}…
Question Number 5236 by sanusihammed last updated on 02/May/16 $${find}\:{the}\:{range}\:{and}\:{domain}\:{of}\: \\ $$$$\left({i}\right)\:\:{y}\:=\:\mid−{x}\mid \\ $$$$\left({ii}\right)\:{y}\:=\:\mid{x}−\mathrm{5}\mid \\ $$ Answered by FilupSmith last updated on 02/May/16 $$\left({i}\right) \\…
Question Number 5235 by sanusihammed last updated on 02/May/16 $${Find}\:{the}\:{range}\:{and}\:{domain}\:{of}\: \\ $$$${y}\:=\:\frac{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{10}\right)}{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}} \\ $$ Answered by Yozzii last updated on 02/May/16 $${x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}=\left({x}+\mathrm{3}\right)^{\mathrm{2}}…
Question Number 136304 by aurpeyz last updated on 20/Mar/21 $$\int{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\:\int\:{x}^{\mathrm{2}} \:\left({x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:\right)\:{dx}\: \\…
Question Number 5234 by sanusihammed last updated on 02/May/16 $${Show}\:{that}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:.\:\:\mid{x}\mid\:\:=\:\:{odd} \\ $$ Answered by prakash jain last updated on 02/May/16 $${a}.\:{x}\geqslant\mathrm{0} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} \centerdot{x}={x}^{\mathrm{3}}…
Question Number 70768 by abdusalamyussif@gmail.com last updated on 07/Oct/19 Commented by abdusalamyussif@gmail.com last updated on 07/Oct/19 $$\mathrm{thanks}\:\mathrm{so}\:\mathrm{much}\:\mathrm{sir} \\ $$ Answered by MJS last updated on…
Question Number 5232 by sanusihammed last updated on 02/May/16 $${If}\:{f}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{{x}−\mathrm{2}}\:\:\:\: \\ $$$$\:\:\:\:{x}\rightarrow\mathrm{2} \\ $$$$ \\ $$$$\alpha\:=\:\mathrm{3}\:.\:\Sigma\:=\:\mathrm{0}.\mathrm{1}\:\:\:{find}\:\:\:\delta \\ $$$$ \\ $$$${Alpha}\:=\:\mathrm{3}\:\:\:{Epsalum}\:=\:\mathrm{0}.\mathrm{1}\:{Find}\:{delta} \\ $$ Commented by…
Question Number 136301 by aurpeyz last updated on 20/Mar/21 $$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{9}}}{dx} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\int\:{x}^{\mathrm{2}} \:\left(\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{9}}}\right){dx} \\…