Question Number 310 by 123456 last updated on 25/Jan/15 $$\underset{\mathrm{1}} {\overset{{e}} {\int}}{xe}^{{t}} −\frac{\mathrm{ln}\:{x}}{{x}}{dx} \\ $$ Answered by prakash jain last updated on 20/Dec/14 $$\int{xe}^{{t}} {dx}−\int\frac{\mathrm{ln}\:{x}}{{x}}{dx}…
Question Number 131383 by EDWIN88 last updated on 04/Feb/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{x}^{\mathrm{2}} }{{x}−\mathrm{1}}\right)^{\mathrm{tan}\:\left(\frac{\mathrm{1}}{\:\sqrt{{x}}}\right)} =? \\ $$ Answered by liberty last updated on 04/Feb/21 $$\mathrm{L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}−\mathrm{1}}\right)^{\mathrm{tan}\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\right)}…
Question Number 131377 by Ahmed1hamouda last updated on 04/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 307 by userid1 last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}{te}^{−\mathrm{3}{t}} \mathrm{cos}\:{t}\:{dt} \\ $$ Commented by 123456 last updated on 20/Dec/14 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}{te}^{−\mathrm{3}{t}}…
Question Number 65841 by Rio Michael last updated on 04/Aug/19 $$\:\frac{{d}}{{dx}}\left(\frac{{tan}\:^{\mathrm{2}} {x}}{\mathrm{1}\:+\:{cos}\:{x}}\right)\:=? \\ $$ Commented by som(math1967) last updated on 05/Aug/19 $${MJS}\:{Sir}\:{it}\:{is}\:{my}\:{way} \\ $$$$\frac{{d}}{{dx}}\left(\frac{{sec}^{\mathrm{2}} {x}−\mathrm{1}}{\mathrm{1}+{cosx}}\right)=\frac{{d}}{{dx}}\left\{\frac{\mathrm{1}−{cos}^{\mathrm{2}}…
Question Number 304 by 123456 last updated on 20/Dec/14 $${u}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\frac{\partial{u}}{\partial{y}}+\frac{\partial{u}}{\partial{x}}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+\mathrm{2}{xu}=\mathrm{0} \\ $$ Commented by prakash jain last updated on 20/Dec/14…
Question Number 131373 by EDWIN88 last updated on 10/Feb/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left[\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} }\:+\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}}\:−\mathrm{2}{x}\:\right]=? \\ $$ Answered by aleks041103 last updated on 04/Feb/21 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left[\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}}…
Question Number 303 by 123456 last updated on 25/Jan/15 $${f}\left({x},{y},{z}\right)=\frac{{y}^{\mathrm{2}} {z}^{\mathrm{3}} }{\mathrm{1}−{x}}+\frac{{xz}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{2}} }+\frac{{xy}^{\mathrm{2}} }{\mathrm{1}−{z}^{\mathrm{3}} } \\ $$$$\mathrm{find} \\ $$$$\frac{\partial{f}}{\partial{x}}+\frac{\partial{f}}{\partial{y}}+\frac{\partial{f}}{\partial{z}} \\ $$ Answered by prakash…
Question Number 131374 by shaker last updated on 04/Feb/21 Answered by MJS_new last updated on 04/Feb/21 $${n}!\approx\left(\frac{{n}}{\mathrm{e}}\right)^{{n}} \sqrt{\mathrm{2}\pi{n}} \\ $$$$\left(\frac{\left(\mathrm{4}{n}\right)!}{\left(\mathrm{3}{n}\right)!}\right)^{\mathrm{1}/{n}} \approx\left(\frac{\left(\frac{\mathrm{4}{n}}{\mathrm{e}}\right)^{\mathrm{4}{n}} \sqrt{\mathrm{8}\pi{n}}}{\left(\frac{\mathrm{3}{n}}{\mathrm{e}}\right)^{\mathrm{3}{n}} \sqrt{\mathrm{6}\pi{n}}}\right)^{\mathrm{1}/{n}} =\frac{\left(\frac{\mathrm{4}{n}}{\mathrm{e}}\right)^{\mathrm{4}} }{\left(\frac{\mathrm{3}{n}}{\mathrm{e}}\right)^{\mathrm{3}}…
Question Number 65837 by mathmax by abdo last updated on 04/Aug/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{−\infty} ^{\infty} \:\frac{{dx}}{\mathrm{1}+{ix}}\:\:{and}\:\int_{−\infty} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}−{ix}} \\ $$$$\left.\mathrm{2}\right){deduce}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}+{ix}^{\mathrm{2}}…