Question Number 70756 by MJS last updated on 07/Oct/19 $$\mathrm{I}\:\mathrm{cannot}\:\mathrm{understand}\:\mathrm{all}\:\mathrm{those}\:\mathrm{who}\:\mathrm{post} \\ $$$$\mathrm{questions}\:\mathrm{like}\:\int{x}^{\Gamma\left({x}^{\mathrm{2}} \right)} \mathrm{cos}\:\sqrt[{{x}}]{\mathrm{log}_{\varpi+{x}} \:{x}^{\mathrm{2}\pi\mathrm{i}} }{dx}=? \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{few}\:\mathrm{minutes}\:\mathrm{later}\:\frac{\mathrm{5}}{\mathrm{3}}×\frac{\mathrm{2}+\mathrm{1}}{\mathrm{9}−\mathrm{4}}=? \\ $$$$\mathrm{I}\:\mathrm{mean},\:\mathrm{are}\:\mathrm{you}\:\mathrm{serious}? \\ $$ Commented by Rio…
Question Number 70757 by MJS last updated on 08/Oct/19 $$. \\ $$ Commented by TawaTawa last updated on 07/Oct/19 $$\mathrm{Sir},\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{the}\:\mathrm{question}\:\mathrm{number}\:\mathrm{of}\:\mathrm{a}\:\mathrm{question}\:\mathrm{you}\:\mathrm{solved} \\ $$$$\mathrm{sometimes}. \\ $$$$ \\…
Question Number 5216 by Yozzii last updated on 01/May/16 $${Let}\:{p}_{{j}} \:{represent}\:{the}\:{j}−{th}\:{prime}\:{number}. \\ $$$${Now},\:{define}\:{the}\:{number}\:{n}\:{whose} \\ $$$${decimal}\:{representation}\:{is}\:{written}\:{out} \\ $$$${in}\:{terms}\:{of}\:{p}_{{j}} \:\left({j}\in\mathbb{N}\right)\:{in}\:{the}\:{following} \\ $$$${way}: \\ $$$${n}=\mathrm{0}.{p}_{\mathrm{1}} {p}_{\mathrm{2}} {p}_{\mathrm{3}} {p}_{\mathrm{4}}…
Question Number 136284 by liberty last updated on 20/Mar/21 $${What}\:{is}\:{shortest}\:{distance}\: \\ $$$${from}\:{A}\left(\mathrm{3},\mathrm{8}\right)\:{to}\:{the}\:{circle}\: \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{6}{y}\:=\:\mathrm{12}\: \\ $$ Answered by EDWIN88 last updated on 20/Mar/21…
Question Number 5214 by sanusihammed last updated on 30/Apr/16 $${If}\:{cos}\theta\:=\:{x}\:\:\:{and}\:\:{sin}\mathrm{60}\:=\:\mathrm{0}.\mathrm{5} \\ $$$${Find}\:{the}\:{value}\:{of}\:\theta \\ $$ Commented by Rasheed Soomro last updated on 01/May/16 $$\mathrm{sin60}\neq\mathrm{0}.\mathrm{5} \\ $$…
Question Number 70746 by Rio Michael last updated on 07/Oct/19 Commented by Rio Michael last updated on 07/Oct/19 $${from}\:{the}\:{above}\:{circuit} \\ $$$$\left.{a}\right){calculate}\:{the}\:{current}\:{flowing}\:{through}\:{the}\:{resistor}\:{R} \\ $$$$\left.{b}\right)\:{find}\:{the}\:{value}\:{of}\:{R} \\ $$$$\left.{c}\right)\:{find}\:{the}\:{emf}\:{E}\:…
Question Number 136283 by JulioCesar last updated on 20/Mar/21 Answered by Ar Brandon last updated on 20/Mar/21 $$\int\mathrm{e}^{\mathrm{g}\left(\mathrm{x}\right)} \left[\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}'\left(\mathrm{x}\right)+\mathrm{f}\:'\left(\mathrm{x}\right)\right]\mathrm{dx}=\mathrm{e}^{\mathrm{g}\left(\mathrm{x}\right)} \mathrm{f}\left(\mathrm{x}\right) \\ $$ Terms of Service…
Question Number 5208 by sanusihammed last updated on 30/Apr/16 $${If}\:{y}\:=\:{x}!\: \\ $$$$ \\ $$$${Find}\:\frac{{dy}}{{dx}} \\ $$ Commented by FilupSmith last updated on 30/Apr/16 $${x}!=\Gamma\left({x}+\mathrm{1}\right) \\…
Question Number 70742 by Joel122 last updated on 07/Oct/19 $$\mathrm{Prove}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{x}\:−\:{a}\:\mathrm{cos}\:\left({x}\right)\:−\:{b} \\ $$$$\mathrm{has}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\mathrm{for}\:\forall{a},{b}\:\in\:\mathbb{R} \\ $$ Commented by kaivan.ahmadi last updated on 07/Oct/19 $${x}−{acosx}−{b}=\mathrm{0}\Rightarrow{x}−{b}={acosx} \\ $$$${y}_{\mathrm{1}} ={x}−{b}…
Question Number 5207 by FilupSmith last updated on 30/Apr/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{S}−\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}!\right)}{{n}}−\mathrm{1}={L} \\ $$$${S}\in\mathbb{R},\:\:{S}>\mathrm{0} \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{can}\:\mathrm{we}\:\mathrm{tell}\:\mathrm{about}\:{L}? \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{limit}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{positive}/\mathrm{negative}?…