Question Number 164716 by cortano1 last updated on 21/Jan/22 $$\:\:\:{find}\:{minimum}\:{value}\:{of}\: \\ $$$$\:{f}\left({x}\right)=\mathrm{4sin}\:\mathrm{2}{x}−\mathrm{5sin}\:{x}−\mathrm{5cos}\:{x}+\mathrm{6} \\ $$ Answered by bobhans last updated on 21/Jan/22 $$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4cos}\:\left(\frac{\pi}{\mathrm{2}}−\mathrm{2x}\right)−\mathrm{5}\sqrt{\mathrm{2}}\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{x}\right)+\mathrm{6} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4cos}\:\mathrm{2}\left(\frac{\pi}{\mathrm{4}}−\mathrm{x}\right)−\mathrm{5}\sqrt{\mathrm{2}}\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{x}\right)+\mathrm{6} \\…
Question Number 164671 by mnjuly1970 last updated on 20/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:\:{solve}\: \\ $$$$\:\:\:\:\:\:{cos}^{\:\mathrm{3}} \left({x}\right)\:+\:{sin}^{\:\mathrm{2}} \left({x}\right)\:=\:\frac{\mathrm{7}}{\mathrm{8}}\: \\ $$$$\:\:\:\:\:\:\:\:\:{adopted}\:{from}\:{youtube}\:… \\ $$$$ \\ $$ Commented by MJS_new…
Question Number 164653 by mnjuly1970 last updated on 20/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:\:{solve} \\ $$$$\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}^{\:\mathrm{2}} \left(\:{x}\:\right).\:{tanh}^{\:−\mathrm{1}} \left(\:{x}\:\:\right)}{{x}}{dx}\:=? \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({tanh}^{−\mathrm{1}} \left({x}\right)\right)^{\:\mathrm{2}} }{\mathrm{1}+{x}}\:=\:? \\…
Question Number 164547 by mnjuly1970 last updated on 21/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:\:{prove} \\ $$$$\: \\ $$$$\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\sqrt{{x}}}{\left(\:\mathrm{1}+{x}\:+{x}^{\:\mathrm{2}} \right)^{\:\mathrm{3}} \:}\:{dx}\:\overset{?} {=}\:\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}}\: \\ $$$$\:\:\:\:\:\:−−{m}.{n}−−\: \\ $$$$…
Question Number 99003 by bramlex last updated on 18/Jun/20 $${Given}\:\mathrm{5}{x}−\mathrm{3}{y}=\mathrm{6}\:.\:{find}\:{min}\:{value} \\ $$$${of}\:\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \:? \\ $$ Answered by bobhans last updated on 18/Jun/20 $$\mathrm{let}\:\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 33407 by NECx last updated on 15/Apr/18 $${if}\:{y}={x}!\:{find}\:{dy}/{dx} \\ $$ Answered by MJS last updated on 15/Apr/18 $$\mathrm{for}\:{x}\in\mathbb{N}\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$\mathrm{if}\:\mathrm{we}\:\mathrm{use} \\ $$$${y}={x}!=\Gamma\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty}…
Question Number 33406 by NECx last updated on 15/Apr/18 $${Find}\:{the}\:{half}\:{derivative}\:{of}\:{y}=\mathrm{ln}\:{x} \\ $$ Commented by MJS last updated on 15/Apr/18 $$\mathrm{what}'\mathrm{s}\:\mathrm{a}\:\mathrm{half}\:\mathrm{derivate}? \\ $$ Commented by NECx…
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Question Number 164462 by ajfour last updated on 17/Jan/22 $${Find}\:{x},\:{such}\:{that}\:{f}\left({x}\right)\:{is}\:{minimum}. \\ $$$${f}\left({x}\right)=\left\{\frac{\sqrt{{c}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{{c}−{x}}−\left({c}−{x}\right)\right\}^{\mathrm{2}} \\ $$ Commented by ajfour last updated on 17/Jan/22 $${did}. \\…
Question Number 98895 by bramlex last updated on 17/Jun/20 $${Is}\:\frac{{dy}}{{dx}}\:{if}\:{y}^{\mathrm{3}} +{x}^{\mathrm{3}} −\mathrm{2}{x}=\mathrm{1}\:?\: \\ $$ Answered by bramlex last updated on 17/Jun/20 Answered by mathmax by…