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 $$\int\:{x}^{\mathrm{2}} \:\left(\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{9}}}\right){dx} \\…
Question Number 136300 by liberty last updated on 20/Mar/21 $${Let}\:{vector}\:\overset{\rightarrow} {{a}}\:,\:\overset{\rightarrow} {{b}}\:{and}\:\overset{\rightarrow} {{c}}\:{such}\:{that} \\ $$$$\mid\overset{\rightarrow} {{a}}\mid=\mid\overset{\rightarrow} {{b}}\mid=\frac{\mid\overset{\rightarrow} {{c}}\mid}{\mathrm{2}}\:{and}\:\overset{\rightarrow} {{a}}×\left(\overset{\rightarrow} {{a}}×\overset{\rightarrow} {{c}}\right)+\overset{\rightarrow} {{b}}=\mathrm{0} \\ $$$${find}\:{the}\:{acute}\:{angle}\:{between}\:\overset{\rightarrow} {{a}}\:{and}\:\overset{\rightarrow}…
Question Number 136303 by SOMEDAVONG last updated on 20/Mar/21 $$\mathrm{If}\:\mathrm{x}^{\mathrm{3}} −\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:\mathrm{1}\:.\mathrm{compute}\:\left(\mathrm{2}+\sqrt{\mathrm{5}}\right)\mathrm{x}^{\mathrm{6}} −\:\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{5}}\right)\mathrm{x}^{\mathrm{6}} }\:=\:? \\ $$ Answered by mr W last updated on 20/Mar/21 $${x}^{\mathrm{6}}…
Question Number 5226 by sanusihammed last updated on 02/May/16 $${Find}\:{b}\:{in}\:{terms}\:{of}\:{a}\:{if}\:\sqrt{{a}\frac{{a}}{{b}}}\:\:\:=\:\:\left(\frac{{a}}{{b}}\right)^{\frac{\mathrm{1}}{{a}}} \:\:\:\:.\:\:{where}\:{a}\:{and}\:{b}\:{are} \\ $$$${whole}\:{numbers}.\:\: \\ $$ Commented by prakash jain last updated on 02/May/16 $$\left(\frac{{ab}+{a}}{{b}}\right)^{\mathrm{1}/\mathrm{2}} =\left(\frac{{a}}{{b}}\right)^{\mathrm{1}/{a}}…
Question Number 136293 by mr W last updated on 20/Mar/21 $${the}\:{sides}\:{of}\:{a}\:{triangle}\:{are}\:\mathrm{5},\mathrm{7},\mathrm{10}\:{cm}. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{largest}\:{equilateral}\:{triangle} \\ $$$${which}\:{circumscribes}\:{the}\:{given}\:{triangle}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{smallest}\:{equilateral}\:{triangle} \\ $$$${which}\:{inscribes}\:{the}\:{given}\:{triangle}. \\ $$ Commented by mr W…
Question Number 136295 by mnjuly1970 last updated on 20/Mar/21 $$\:\:\:\:\:\:….{nice}\:\:{calculus}… \\ $$$${prove}\::: \\ $$$$\mathrm{1}\:::\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}^{−\mathrm{1}} \left(\sqrt{{tan}\left({x}\right)}\:\right)}{{tan}\left({x}\right)}{dx}=\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}+\sqrt{\mathrm{2}}\:\right) \\ $$$$\mathrm{2}::\Omega=\int_{−\pi} ^{\:\pi} \frac{{e}^{\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)} {cos}\left({sin}\left({x}\right)\right)}{{e}^{{x}} +{e}^{{sin}\left({x}\right)} }{dx}=\pi \\…