Question Number 137275 by mnjuly1970 last updated on 31/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:……{complex}\:\:{analysis}….. \\ $$$$\:\:\:\:{if}\:,\:\:{f}\left(\alpha,{n},{x}\right)=\frac{{d}^{\:{n}} }{{dx}^{{n}} }\left(\alpha^{{x}} \right)\:\:,\:{x}\in\mathbb{C} \\ $$$$\:\:\:\:\:\alpha\in\mathbb{C}−\left\{\mathrm{0}\right\}\:,\:{n}\in\mathbb{C}−\mathbb{Z}^{−} \cup\left\{\mathrm{0}\right\} \\ $$$$\:\:\:\:\:{and}\:\:{g}\left({n},{x}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left(\alpha,{n},{x}\right){d}\alpha \\ $$$$\:\:\:\:\:{then}\:\:{find}\:\:{the}\:{value}\:{of}\:… \\…
Question Number 137269 by mohssinee last updated on 31/Mar/21 Commented by mohssinee last updated on 31/Mar/21 $${n}\in\mathbb{N}^{\ast} \\ $$ Answered by aleks041103 last updated on…
Question Number 71729 by peter frank last updated on 19/Oct/19 $${find}\:{dU}\:\:\:{if}\:\:\:{U}={x}^{\mathrm{2}} {e}^{\frac{{x}}{{y}}} \\ $$$$ \\ $$ Commented by peter frank last updated on 19/Oct/19 $${thank}\:{you}…
Question Number 6192 by sanusihammed last updated on 17/Jun/16 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{circle}\:{circumscribing}\:{the}\:{triangle}\:{form}\:{by}\: \\ $$$${lines}\:\:\mathrm{3}{x}\:+\:{y}\:−\:\mathrm{5}\:=\:\mathrm{0},\:{x}\:+\:{y}\:+\:\mathrm{1}\:=\:\mathrm{0},\:{and}\:\mathrm{2}{x}\:+\:{y}\:−\:\mathrm{4}\:=\:\mathrm{0} \\ $$ Answered by Rasheed Soomro last updated on 18/Jun/16 $$\mathrm{3}{x}\:+\:{y}\:−\:\mathrm{5}\:=\:\mathrm{0}……\left({i}\right) \\ $$$${x}\:+\:{y}\:+\:\mathrm{1}\:=\:\mathrm{0}……..\left({ii}\right)…
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Question Number 6189 by enigmeyou last updated on 17/Jun/16 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\lfloor{x}^{\lfloor{xlnx}\rfloor} \rfloor=? \\ $$ Commented by FilupSmith last updated on 18/Jun/16 $$\lfloor{x}\rfloor\:\mathrm{is}\:\mathrm{only}\:\mathrm{really}\:\mathrm{applicable}\:\mathrm{for}\:\mathrm{non} \\ $$$$\mathrm{integers}.\:\lfloor{x}\mathrm{ln}{x}\rfloor\:\mathrm{is}\:\mathrm{only}\:\mathrm{applicable}\:\mathrm{if} \\…
Question Number 6186 by sanusihammed last updated on 17/Jun/16 $${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:? \\ $$ Commented by Rasheed Soomro last updated on 17/Jun/16 $${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:?…
Question Number 6183 by Rasheed Soomro last updated on 17/Jun/16 $${Show}\:{that} \\ $$$$\mathrm{180}°−\mathrm{2cos}^{−\mathrm{1}} \:\frac{\mathrm{2}}{\:\sqrt{\mathrm{13}}}=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{12}}{\mathrm{13}}\right) \\ $$ Answered by Yozzii last updated on 18/Jun/16 $$\pi−\mathrm{2}{acos}\left(\mathrm{2}/\sqrt{\mathrm{13}}\right)={asin}\left(\mathrm{12}/\mathrm{13}\right)…
Question Number 137252 by mey3nipaba last updated on 31/Mar/21 $$\mathrm{Decompose}\:\mathrm{the}\:\mathrm{function}\:\mathrm{P}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{6x}^{\mathrm{2}} +\mathrm{20x}+\mathrm{6}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\: \\ $$$$\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$ Answered by bemath last updated on…