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Author: Tinku Tara

2-x-log-2-3-12-find-x-

Question Number 205817 by hardmath last updated on 31/Mar/24 $$\mathrm{2}^{\:\boldsymbol{\mathrm{x}}\:+\:\boldsymbol{\mathrm{log}}_{\mathrm{2}} \:\mathrm{3}} \:=\:\mathrm{12}\:\:\Rightarrow\:\:\mathrm{find}:\:\:\mathrm{x}\:=\:? \\ $$ Answered by A5T last updated on 31/Mar/24 $$\left(\mathrm{2}^{{x}} \right)\left(\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{3}} \right)=\mathrm{12}\Rightarrow\left(\mathrm{2}^{{x}}…

can-t-Solve-Differantial-Equation-Diff-Equa-dy-t-dt-2-4y-t-8t-2-32t-28-Sadly-it-s-impossible-to-obtain-an-exact-closed-form-expression-of-the-Solution-of-Diff-Equa-But-if-the-Runge-Kut

Question Number 205833 by MathedUp last updated on 31/Mar/24 $$\mathrm{can}'\mathrm{t}\:\mathrm{Solve}\:\mathrm{Differantial}\:\mathrm{Equation} \\ $$$$\mathrm{Diff}\:\mathrm{Equa}\::\:\left(\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\right)^{\mathrm{2}} +\mathrm{4}{y}\left({t}\right)=\mathrm{8}{t}^{\mathrm{2}} −\mathrm{32}{t}+\mathrm{28}…. \\ $$$$\mathrm{Sadly}\:\mathrm{it}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{closed}−\mathrm{form}\:\mathrm{expression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Solution}\:\mathrm{of}\:\mathrm{Diff}\:\mathrm{Equa} \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{the}\:\mathrm{Runge}−\mathrm{Kutta}\:\mathrm{method}\:\mathrm{is}\:\mathrm{used}. \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{at}\:\mathrm{any}\:\mathrm{one}\:\mathrm{point}\:\mathrm{can}\:\mathrm{be}\:\mathrm{estimated} \\ $$ Commented…

f-x-2-4f-x-8x-2-32x-28-f-x-

Question Number 205825 by tri26112004 last updated on 31/Mar/24 $$\left[{f}'\left({x}\right)\right]^{\mathrm{2}} +\mathrm{4}{f}\left({x}\right)=\mathrm{8}{x}^{\mathrm{2}} −\mathrm{32}{x}+\mathrm{28} \\ $$$$\Rightarrow{f}\left({x}\right)=¿ \\ $$ Commented by mr W last updated on 31/Mar/24 $${f}\left({x}\right)={x}^{\mathrm{2}}…

f-0-3-x-gt-0-f-0-3-f-3-8-3-0-f-x-2-f-x-1-dx-4-3-f-2-

Question Number 205826 by tri26112004 last updated on 31/Mar/24 $$\underset{\left[\mathrm{0};\mathrm{3}\right]} {{f}}\left({x}\right)>\mathrm{0} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{8} \\ $$$$\underset{\mathrm{0}} {\int}^{\mathrm{3}} \frac{\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{{f}\left({x}\right)+\mathrm{1}}{dx}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$${f}\left(\mathrm{2}\right)=¿ \\ $$ Terms…

Question-205772

Question Number 205772 by mr W last updated on 30/Mar/24 Answered by MM42 last updated on 30/Mar/24 $${S}_{{n}} =\left(\sqrt{\mathrm{1}×\mathrm{2}}−\mathrm{1}\right) \\ $$$$+\left(\sqrt{\mathrm{2}×\mathrm{3}}−\sqrt{\mathrm{1}×\mathrm{2}}−\mathrm{1}\right) \\ $$$$+\left(\sqrt{\mathrm{3}×\mathrm{4}}−\sqrt{\mathrm{2}×\mathrm{3}}−\mathrm{1}\right) \\ $$$$\vdots…