Question Number 64968 by ajfour last updated on 23/Jul/19 Commented by ajfour last updated on 25/Jul/19 $${Instead}\:{let}\:\:{y}={Ax}^{\mathrm{2}} \:,\:{find}\:{side} \\ $$$${length}\:{of}\:{such}\:{a}\:{rhombus}\:{that} \\ $$$${fits}\:{in},\:{the}\:{way}\:{shown}.\:{Also} \\ $$$${find}\:{A}.\:\:\:\:\:\:\: \\…
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Question Number 130496 by Adel last updated on 26/Jan/21 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}!\right)=? \\ $$ Answered by MJS_new last updated on 26/Jan/21 $${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$ \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{mean}\:{x}!=\Gamma\:\left({x}+\mathrm{1}\right) \\…
Question Number 64955 by Tony Lin last updated on 23/Jul/19 $${prove}\:{that}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}\centerdot\frac{\left({k}+\mathrm{1}\right)!}{\mathrm{2}^{{k}+\mathrm{1}} }=\frac{\left({n}+\mathrm{2}\right)!}{\mathrm{2}^{{n}+\mathrm{1}} }−\mathrm{1} \\ $$ Commented by ~ À ® @ 237 ~…
Question Number 130486 by benjo_mathlover last updated on 26/Jan/21 $$\:\int_{\mathrm{0}} ^{\:{x}} \:\frac{\mathrm{cos}\:{t}\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{3}} \:{t}}}{\left(\mathrm{sin}\:{x}−\mathrm{sin}\:{t}\right)^{\mathrm{3}/\mathrm{4}} }\:{dt}\:? \\ $$ Answered by MJS_new last updated on 26/Jan/21 $$\int\mathrm{cos}\:{t}\:\left(\frac{\mathrm{sin}\:{t}}{\mathrm{sin}\:{x}\:−\mathrm{sin}\:{t}}\right)^{\mathrm{3}/\mathrm{4}} {dt}=…
Question Number 64951 by naka3546 last updated on 23/Jul/19 Answered by mr W last updated on 23/Jul/19 Commented by mr W last updated on 23/Jul/19…
Question Number 64949 by Tony Lin last updated on 23/Jul/19 Commented by Tony Lin last updated on 23/Jul/19 $${find}\:{x} \\ $$ Answered by MJS last…
Question Number 130485 by benjo_mathlover last updated on 26/Jan/21 $$\:\digamma\:=\:\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}\:} \mathrm{ln}\:\left({x}\right)\mathrm{cos}\:\left({x}\right){e}^{−{x}} \:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $${I}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 130483 by benjo_mathlover last updated on 26/Jan/21 Answered by EDWIN88 last updated on 10/Feb/21 $$\left(\mathrm{5}\right)\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}cos}\:\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{cos}\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}f}\left(\mathrm{x}\right)=\mathrm{cos}\:\left(−\mathrm{1}\right)=\mathrm{cos}\:\mathrm{1} \\ $$ Terms of Service Privacy…