Question Number 158293 by mnjuly1970 last updated on 02/Nov/21 $$ \\ $$$$\:\:\:\:\:{question}# \\ $$$$\left.\mathrm{If}\:,\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}^{\:\mathrm{4}} \right)}{{x}}\:{dx}=\:{a}\:\zeta\:{b}\right) \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:,\:\:\:\:\:{a}\:\:,\:{b}\:\:. \\ $$$$ \\ $$$$ \\…
Question Number 158259 by cortano last updated on 01/Nov/21 $${Given}\:{x},{y}\in\mathbb{R}^{+} \:{and}\:\left(\frac{{x}}{\mathrm{5}}+\frac{{y}}{\mathrm{3}}\right)\left(\frac{\mathrm{5}}{{x}}+\frac{\mathrm{3}}{{y}}\right)=\mathrm{139}. \\ $$$$\:{If}\:{maximum}\:{and}\:{minimum} \\ $$$$\:{of}\:\frac{{x}+{y}}{\:\sqrt{{xy}}\:}\:{is}\:{M}\:{and}\:{n}\:{respectively}, \\ $$$${then}\:{what}\:{the}\:{value}\:{of}\:\mathrm{3}{M}−\mathrm{4}{n}. \\ $$ Commented by tounghoungko last updated on…
Question Number 158156 by mnjuly1970 last updated on 31/Oct/21 $$ \\ $$$$\:\:\:{solve}\:: \\ $$$$\left(\:{x}^{\:\mathrm{2}} +{x}\:−\mathrm{6}\right)^{\:\mathrm{3}} +\:\left(\mathrm{7}{x}^{\:\mathrm{2}} −\mathrm{9}{x}\:−\mathrm{2}\right)^{\:\mathrm{3}} −\mathrm{512}\left({x}^{\mathrm{2}} −{x}−\mathrm{1}\right)^{\:\mathrm{3}} =\mathrm{0} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:=\:? \\…
Question Number 92619 by jagoll last updated on 08/May/20 $$\mathrm{find}\:\mathrm{x}\:\mathrm{in}\:\mathrm{closset}\:\mathrm{interval}\: \\ $$$$\left[\:−\mathrm{4},\mathrm{3}\:\right]\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{3x}−\frac{\mathrm{9}}{\mathrm{2}}\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\right)− \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\right)\sqrt{\mathrm{9}−\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{maximum} \\ $$ Terms of Service…
Question Number 158064 by zainaltanjung last updated on 30/Oct/21 $$ \\ $$$$ \\ $$$$\mathrm{Make}\:\mathrm{tangen}\:\mathrm{line}\:\mathrm{at}\:\mathrm{point}\: \\ $$$$\left(\mathrm{2},\mathrm{3}\right).\: \\ $$$$ \\ $$ Answered by ajfour last updated…
Question Number 158060 by zainaltanjung last updated on 30/Oct/21 Answered by puissant last updated on 30/Oct/21 $$\left.\mathrm{1}\right) \\ $$$$\frac{{dy}}{{dx}}\:=\:\mathrm{2}{x}+\mathrm{3}\:;\:{x}=\mathrm{3}\:\Rightarrow\:\frac{{dy}}{{dx}}=\:\mathrm{9} \\ $$$$\left.\mathrm{2}\right) \\ $$$$\frac{{dy}}{{dx}}=\:\mathrm{12}{x}^{\mathrm{3}} +\mathrm{15}{x}^{\mathrm{2}} +\mathrm{1}\:;\:{x}=\mathrm{2}\:\Rightarrow\:\frac{{dy}}{{dx}}=\mathrm{157}…
Question Number 158049 by zainaltanjung last updated on 30/Oct/21 $$\mathrm{Find}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{this}\:\mathrm{function} \\ $$$$\left.\mathrm{1}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}.\mathrm{sin}\:\mathrm{x} \\ $$$$\left.\mathrm{2}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{e}^{\mathrm{5x}} .\:\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{3x}\right) \\ $$$$\left.\mathrm{3}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{3}^{\mathrm{3x}} .\left(\mathrm{2x}−\mathrm{1}\right) \\ $$$$\left.\mathrm{4}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{2}}{\mathrm{4x}+\mathrm{1}} \\ $$ Answered…
Question Number 92510 by john santu last updated on 07/May/20 $$\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} +\mathrm{2}}\:\left(\mathrm{sin}\:\mathrm{2x}\right)\:?\: \\ $$ Commented by john santu last updated on 08/May/20 $$\mathrm{consider}\:\mathrm{y}_{\mathrm{p}} \:=\:{x}\mathrm{sin}\:\mathrm{2}{x} \\…
Question Number 26947 by prakash jain last updated on 31/Dec/17 $$\frac{{d}}{{dx}}\mathrm{ln}\:\left(\Gamma\left({x}+\mathrm{1}\right)\right)=? \\ $$ Commented by abdo imad last updated on 31/Dec/17 $${we}\:{know}\:{that}\:\Gamma\left({x}+\mathrm{1}\right)={x}\:\Gamma\left({x}\right)\:{with}\:{x}>\mathrm{0} \\ $$$$\Rightarrow{ln}\left(\Gamma\left({x}+\mathrm{1}\right)\right)\:=\:\:{lnx}\:+{ln}\left(\Gamma\left({x}\right)\right) \\…
Question Number 26941 by Mr eaay last updated on 31/Dec/17 $${show}\:{that}\:{the}\:{rectangular}\:{solid}\:\:{of}\: \\ $$$${naximum}\:{volume}\:{that}\:{can}\:{be}\:{inscribed} \\ $$$${into}\:{a}\:{sphere}\:{is}\:{a}\:{cube} \\ $$ Answered by mrW1 last updated on 01/Jan/18 $${x}^{\mathrm{2}}…