Question Number 114304 by mnjuly1970 last updated on 18/Sep/20 $$\:\:\:\:\:\:\:{calculus}….. \\ $$$$\:{evaluate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{−\mathrm{1}} ^{\:\mathrm{1}} {xln}\left(\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\mathrm{3}^{{x}} +\mathrm{6}^{{x}} \right){dx}\:=???\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Commented…
Question Number 179741 by mnjuly1970 last updated on 01/Nov/22 $$ \\ $$$$\:\:\:\:\:{prove}\:\:{that} \\ $$$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty\:} \frac{\:\sqrt{{x}}}{\mathrm{1}\:+\mathrm{7}{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{4}} }\:{dx}\:=\:\frac{\pi}{\:\sqrt{\:\mathrm{90}}}\:\: \\ $$$$ \\ $$ Terms…
Question Number 114181 by bemath last updated on 17/Sep/20 $${Given}\:{a}\:{function}\: \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{4}{x}+\frac{\mathrm{4}}{{x}}\:;\:{where}\:{x}>\mathrm{0}. \\ $$$${find}\:{the}\:{minimum}\:{value}\:{of}\:{f}\left({x}\right) \\ $$ Answered by bobhans last updated on 17/Sep/20…
Question Number 114099 by mnjuly1970 last updated on 17/Sep/20 $$\:\:\:….\:\:{mathematical}\:\:{analysis}….\:\: \\ $$$$\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\:\frac{\mathrm{3}^{{n}} −\mathrm{1}}{\mathrm{4}^{{n}} }\right)\zeta\left({n}+\mathrm{1}\right)\:=\pi\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970}# \\ $$$$ \\…
Question Number 114066 by john santu last updated on 17/Sep/20 $${Given}\:{f}\left({x}\right)=\mathrm{7}+\mathrm{cos}\:\mathrm{2}{x}+\mathrm{2sin}\:^{\mathrm{2}} {x} \\ $$$${find}\:{f}^{\left(\mathrm{10}\right)} \left({x}\right)\:? \\ $$ Commented by bemath last updated on 17/Sep/20 $${f}\left({x}\right)=\mathrm{7}+\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 113952 by bemath last updated on 16/Sep/20 $${find}\:{all}\:{asymptotes}\:{of}\:{function} \\ $$$${f}\left({x}\right)=\left(\frac{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{5}}{{x}^{\mathrm{2}} +{x}+\mathrm{3}}\right)^{{x}+\mathrm{5}} \\ $$ Commented by MJS_new last updated on 16/Sep/20 $$\mathrm{forgot}\:\mathrm{the}\:\mathrm{squares}??? \\…
Question Number 179428 by nadovic last updated on 29/Oct/22 $$\mathrm{Find}\:\:\frac{{dy}}{{dx}}\:\:\mathrm{if}\:\:{y}\:=\:\mathrm{3sin}^{\mathrm{2}} \left({x}−\mathrm{5}{x}^{\mathrm{2}} \right)\: \\ $$ Answered by cortano1 last updated on 29/Oct/22 $$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{6}\left(\mathrm{1}−\mathrm{10x}\right)\mathrm{sin}\:\left(\mathrm{x}−\mathrm{5x}^{\mathrm{2}} \right)\mathrm{cos}\:\left(\mathrm{x}−\mathrm{5x}^{\mathrm{2}} \right) \\…
Question Number 48307 by MJS last updated on 21/Nov/18 $${f}\left({x}\right)={x}^{{x}^{{x}−\mathrm{1}} } \:\:\:\:\:\left[={x}^{\left({x}^{{x}−\mathrm{1}} \right)} \right] \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{funny}\:\mathrm{one}… \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{2}^{\mathrm{2}} \\ $$$${f}\left(\mathrm{3}\right)=\left(\mathrm{3}^{\mathrm{3}} \right)^{\mathrm{3}} \\ $$$${f}\left(\mathrm{4}\right)=\left(\left(\mathrm{4}^{\mathrm{4}}…
Question Number 48291 by Rio Michael last updated on 21/Nov/18 $${Find}\:{the}\:{exact}\:{value}\:{of}\:\mathrm{0}^{\mathrm{0}} \\ $$ Commented by maxmathsup by imad last updated on 21/Nov/18 $$\mathrm{0}^{\mathrm{0}} ={lim}_{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 179258 by zaheen last updated on 27/Oct/22 $${y}={x}^{{x}^{{x}} } \\ $$$$\frac{{dy}}{{dx}}=? \\ $$ Commented by CElcedricjunior last updated on 30/Oct/22 $$\left.{y}=\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} } =\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}}…