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Author: Tinku Tara

Let-f-1-R-be-a-differentiable-function-such-that-f-1-1-3-and-3-1-x-f-t-dt-x-f-x-x-3-3-x-1-find-tbe-value-of-f-e-

Question Number 204645 by cortano12 last updated on 24/Feb/24 $$\:\:\mathrm{Let}\:{f}\::\:\left[\:\bar {\mathrm{1}}\infty\right)\:\rightarrow\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{differentiable}\: \\ $$$$\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{1}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\: \\ $$$$\:\mathrm{3}\underset{\mathrm{1}} {\overset{\mathrm{x}} {\int}}\:{f}\left({t}\right)\:{dt}\:=\:{x}\:{f}\left({x}\right)−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\:,\mathrm{x}\in\left[\mathrm{1},\infty\right)\: \\ $$$$\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:{f}\left({e}\right)\: \\ $$ Commented by universe…

Question-204647

Question Number 204647 by Engr_Jidda last updated on 24/Feb/24 Answered by Rasheed.Sindhi last updated on 24/Feb/24 $$\left(\frac{{x}}{\mathrm{2}}\right)^{\frac{{x}}{\mathrm{2}}−\mathrm{1}} =\mathrm{3}^{\mathrm{2}} \\ $$$$\Leftarrow\frac{{x}}{\mathrm{2}}=\mathrm{3}\:\wedge\:\frac{{x}}{\mathrm{2}}−\mathrm{1}=\mathrm{2}\Rightarrow{x}=\mathrm{6} \\ $$ Commented by Engr_Jidda…

f-x-1-1-x-1-1-a-ax-ax-8-a-gt-0-x-gt-0-prove-1-lt-f-x-lt-2-

Question Number 204640 by liuxinnan last updated on 24/Feb/24 $${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\sqrt{\frac{{ax}}{{ax}+\mathrm{8}}} \\ $$$${a}>\mathrm{0}\:{x}>\mathrm{0} \\ $$$${prove}\:\mathrm{1}<{f}\left({x}\right)<\mathrm{2} \\ $$ Answered by lepuissantcedricjunior last updated on 26/Feb/24 $$\boldsymbol{{x}}>\mathrm{0}\:\boldsymbol{{a}}>\mathrm{0} \\…

Consider-point-A-inside-a-triangle-with-sides-3-4-and-5-if-d-is-the-sum-of-the-distances-of-this-point-from-the-sides-what-is-the-smallest-value-of-d-

Question Number 204657 by es last updated on 24/Feb/24 $${Consider}\:{point}\:{A}\:{inside}\:{a}\:{triangle} \\ $$$${with}\:{sides}\:\mathrm{3},\mathrm{4}\:{and}\:\mathrm{5}.\:{if}\:{d}\:\:{is}\:{the}\:{sum} \\ $$$$\:{of}\:{the}\:{distances}\:\:{of}\:{this}\:{point}\:{from} \\ $$$${the}\:{sides}.{what}\:{is}\:{the}\:{smallest} \\ $$$${value}\:{of}\:{d}? \\ $$$$ \\ $$ Answered by mr…