Question Number 62220 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{t}^{\mathrm{2}} }{{x}^{\mathrm{6}} \:\:+{t}^{\mathrm{6}} }\:{dt}\:\:\:\:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\left({x}^{\mathrm{6}} \:+{t}^{\mathrm{6}}…
Question Number 127752 by Olaf last updated on 01/Jan/21 $$\mathrm{I}\:\mathrm{wish}\:\mathrm{you}\:\mathrm{an}\:\mathrm{happy}\:\mathrm{new}\:\mathrm{year}\:\mathrm{from}\:\mathrm{Paris}. \\ $$ Commented by mindispower last updated on 01/Jan/21 $${are}\:{you}\:{french}\:{sir}\:? \\ $$ Commented by Dwaipayan…
Question Number 62214 by Rasheed.Sindhi last updated on 17/Jun/19 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{x},\mathrm{y}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right)}{\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right)}=\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right)−\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right) \\ $$ Answered by MJS last updated on 17/Jun/19 $$\mathrm{lcm}\:\left({x},\:{y}\right)=\frac{\mathrm{gcd}^{\mathrm{2}} \:\left({x},\:{y}\right)}{\mathrm{gcd}\:\left({x},{y}\right)\:−\mathrm{1}} \\ $$$$\Rightarrow\:\mathrm{gcd}\:\left({x},{y}\right)=\mathrm{2}\wedge\mathrm{lcm}\:\left({x},\:{y}\right)=\mathrm{4}\:\Rightarrow\:…
Question Number 62213 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\int\int_{{D}} \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} }{dxdydz}\:{with} \\ $$$${D}\:=\left\{\left({x},{y},{z}\right)\in{R}^{\mathrm{3}} \:/\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\:\:{and}\:\:\:\mathrm{2}\leqslant{z}\leqslant\mathrm{3}\:\right\} \\ $$ Commented…
Question Number 127749 by ajfour last updated on 01/Jan/21 Commented by ajfour last updated on 01/Jan/21 $${Find}\:{ratio}\:{of}\:{radius}\:{of}\:{small} \\ $$$${semicircles}\:{of}\:{equal}\:{radii}\:{to} \\ $$$${that}\:{of}\:{outer}\:{semicircle}\:{r}/{R}. \\ $$ Answered by…
Question Number 62211 by Tony Lin last updated on 18/Jun/19 $$\frac{{x}}{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }+\mathrm{3}}{Max}=\frac{\mathrm{5}}{\mathrm{3}}? \\ $$ Commented by MJS last updated on 17/Jun/19 $$\mathrm{what}\:\mathrm{does}\:\mathrm{this}\:\mathrm{mean}? \\ $$ Commented…
Question Number 62210 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{f}\left({x}\right)\:=\left({x}+\mathrm{1}\right)^{{n}} \:{arctan}\left({nx}\right) \\ $$$${calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$ Commented by mathmax by abdo last updated…
Question Number 62209 by maxmathsup by imad last updated on 17/Jun/19 $${find}\:{g}\left({a}\right)\:=\int\left({x}+{a}\right)\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }{dx}\: \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19…
Question Number 62208 by maxmathsup by imad last updated on 17/Jun/19 $${find}\:{f}\left({a}\right)\:=\int\:\:\left({x}−{a}\right)\sqrt{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19…
Question Number 127742 by arash sharifi last updated on 01/Jan/21 $$\int{xdx} \\ $$ Answered by Olaf last updated on 01/Jan/21 $$\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} +\mathrm{C}_{\mathrm{1}} \\ $$$$\mathrm{are}\:\mathrm{you}\:\mathrm{serious}\:?\: \\…