Question Number 1543 by 112358 last updated on 17/Aug/15 $${Let}\:{a},\:{b}\in\mathbb{R}.\:{Show}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid\mid{a}\mid−\mid{b}\mid\mid\leqslant\mid{a}−{b}\mid. \\ $$ Answered by Rasheed Soomro last updated on 18/Aug/15 $$\boldsymbol{\mathrm{Alternative}}\:\boldsymbol{\mathrm{way}}\:,\:\boldsymbol{\mathrm{technically}}\:\boldsymbol{\mathrm{simpler}}. \\ $$$$\mid\mid{a}\mid−\mid{b}\mid\mid\leqslant\mid{a}−{b}\mid………………….\left(\boldsymbol{\mathrm{I}}\right)…
Question Number 132612 by aurpeyz last updated on 15/Feb/21 $$\int{e}^{{x}+{e}^{{x}} } {dx} \\ $$ Answered by Dwaipayan Shikari last updated on 15/Feb/21 $$\int{e}^{{x}} {e}^{{e}^{{x}} }…
Question Number 1540 by Rasheed Soomro last updated on 17/Aug/15 $$\mathrm{Determine}\:\mathrm{three}\:\mathrm{complex}\:\mathrm{numbers}\:\alpha\:,\:\beta\:,\gamma\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha=\beta^{\:\mathrm{2}} \:\:\:\:\:\:\:{but}\:\:\:\:\beta\:\neq\:\alpha^{\:\mathrm{2}} \\ $$$$\beta\:=\:\gamma^{\:\mathrm{2}} \:\:\:\:\:\:{but}\:\:\:\:\:\gamma\:\neq\:\beta^{\:\mathrm{2}} \\ $$$$\gamma\:=\:\alpha^{\:\mathrm{2}\:} \:\:\:\:\:{but}\:\:\:\:\:\alpha\:\neq\:\gamma^{\:\mathrm{2}} \\ $$ Answered by 123456…
Question Number 1539 by 314159 last updated on 17/Aug/15 $$\boldsymbol{\mathrm{Find}}\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}\right)^{\mathrm{4}} }. \\ $$ Answered by 123456 last updated on 17/Aug/15 $$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{4}}…
Question Number 132611 by aurpeyz last updated on 15/Feb/21 $$\int\left({e}^{−\mathrm{2}{x}^{\mathrm{2}} } \right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 67072 by TawaTawa last updated on 22/Aug/19 Answered by mr W last updated on 22/Aug/19 Commented by mr W last updated on 22/Aug/19…
Question Number 1537 by 2closedStringsMeet last updated on 17/Aug/15 $${Show}\:{by}\:{use}\:{of}\:{the}\:{characteristics}\:{of} \\ $$$${a}\:{vector}−{space},\:{that}\:{the}\:{set}\:\overset{\rightarrow} {{x}}\in\mathbb{R}_{+} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{following}\:\mathrm{operations}\:\oplus\:{and}\: \\ $$$${builds}\:{a}\:{vector}−{space}. \\ $$$$\ast{Use}\:{vector}−{space}\:{axioms} \\ $$$$\ast\overset{\rightarrow} {{x}}\oplus\overset{\rightarrow} {{y}}\:\:\:\:{be}\:\:\:\overset{\rightarrow} {{x}}\centerdot\overset{\rightarrow} {{y}}…
Question Number 132610 by liberty last updated on 15/Feb/21 $$\Omega=\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 15/Feb/21 $$\int\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+{sin}^{\mathrm{2}} {x}}{dx}={x}−\int\frac{\mathrm{1}}{\mathrm{1}+{sin}^{\mathrm{2}}…
Question Number 67070 by mRDv143 last updated on 22/Aug/19 Commented by Prithwish sen last updated on 23/Aug/19 $$\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \:\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}}}\:\mathrm{dx}=\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} .\mathrm{x}\:\sqrt{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{1}}}\:\mathrm{dx} \\…
Question Number 67071 by TawaTawa last updated on 22/Aug/19 Commented by Prithwish sen last updated on 22/Aug/19 $$\left.\mathrm{a}\right)\mathrm{The}\:\mathrm{eqn}.\:\mathrm{of}\:\boldsymbol{\mathrm{C}}\:\:\left(\mathrm{x}−\mathrm{8}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \\ $$$$\because\:\boldsymbol{\mathrm{L}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tangent} \\ $$$$\therefore\:\frac{\mathrm{k}.\mathrm{8}−\mathrm{5}.\mathrm{2}−\mathrm{21}}{\:\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{25}}}\:=\:\mathrm{r}…