Question Number 66345 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 808 by sai dinesh last updated on 16/Mar/15 $${if}\:{the}\:{equations}\:{of}\:{the}\:{sides}\:{of}\:{the}\:{triangle}\:{are}\:\mathrm{7}{x}+{y}−\mathrm{10}=\mathrm{0},{x}−\mathrm{2}{y}+\mathrm{5}=\mathrm{0}\:{and}\:{x}+{y}+\mathrm{2}=\mathrm{0},\:{find}\:{the}\:{orhocentre}\:{of}\:{the}\:{triangle} \\ $$ Commented by prakash jain last updated on 16/Mar/15 $${if}\:{the}\:{equations}\:{of}\:{the}\:{sides}\:{of}\:{the}\:{triangle}\:{are}\: \\ $$$$\mathrm{7}{x}+{y}−\mathrm{10}=\mathrm{0},{x}−\mathrm{2}{y}+\mathrm{5}=\mathrm{0}\:{and}\:{x}+{y}+\mathrm{2}=\mathrm{0}, \\…
Question Number 131877 by Dwaipayan Shikari last updated on 09/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left({e}^{\mathrm{2}\pi{n}} −\mathrm{1}\right)} \\ $$ Commented by Dwaipayan Shikari last updated on 09/Feb/21 $${I}\:{have}\:{found}\:…
Question Number 66342 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{U}_{{n}} =\int_{{n}} ^{{n}+\mathrm{2}} \:\:\frac{\left({t}+{n}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{{t}^{\frac{\mathrm{1}}{\mathrm{3}}} }{dt}\:\:{prove}\:{that}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} =\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 131876 by I want to learn more last updated on 09/Feb/21 Answered by EDWIN88 last updated on 09/Feb/21 $$\left(\mathrm{i}\right)\:\mathrm{C}_{\mathrm{8}} ^{\mathrm{10}} \:=\:\frac{\mathrm{10}×\mathrm{9}}{\mathrm{2}×\mathrm{1}}=\mathrm{45}\: \\ $$…
Question Number 806 by 123456 last updated on 16/Mar/15 $${if}\:{p}\left({x}\right)\:{is}\:{a}\:{polynomial}\:{and} \\ $$$${p}\left({x}\right){p}\left(\frac{\mathrm{1}}{{x}}\right)={p}\left({x}\right)+{p}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$$${p}\left(\mathrm{3}\right)=\mathrm{28} \\ $$$${then} \\ $$$${p}\left({x}\right)=? \\ $$$${p}\left(\mathrm{4}\right)=? \\ $$ Commented by 123456…
Question Number 131879 by Study last updated on 09/Feb/21 $${prove}\:{that}\:{sin}\left({n}\pi\right)=\mathrm{0}\:\:\:{if}\:\:\:\:{n}\in\mathbb{Z} \\ $$ Answered by physicstutes last updated on 10/Feb/21 $$\mathrm{prove}\:\mathrm{for}\:{n}\:=\:\mathrm{1} \\ $$$$\mathrm{sin}\:\pi\:=\:\mathrm{0} \\ $$$$\mathrm{assume}\:\mathrm{for}\:{n}=\:{k}\:,\:{k}\:\in\mathbb{Z} \\…
Question Number 66340 by mathmax by abdo last updated on 12/Aug/19 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \left(\mathrm{2}−{x}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 805 by 123456 last updated on 17/Mar/15 $${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$${f}\left({xy}\right)={xf}\left({y}\right)+{yf}\left({x}\right) \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 17/Mar/15…
Question Number 66341 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{k}^{\mathrm{3}} }{\:\sqrt{\left(\mathrm{1}+\left(\frac{{k}}{{n}}\right)^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$ Commented by Prithwish sen…