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Category: Algebra

Question-136741

Question Number 136741 by JulioCesar last updated on 25/Mar/21 Answered by Dwaipayan Shikari last updated on 25/Mar/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}!−\mathrm{1}}{{x}}=\frac{\Gamma\left({x}+\mathrm{1}\right)−\mathrm{1}}{{x}}=\frac{\Gamma'\left({x}+\mathrm{1}\right)}{\mathrm{1}}=\Gamma'\left(\mathrm{1}\right)=−\gamma \\ $$ Terms of Service Privacy…

the-curve-y-f-x-when-f-x-is-a-quadratic-expression-has-a-maximum-value-point-at-1-4-The-curve-touches-the-line-6x-y-13-Find-the-value-of-x-for-which-y-8-

Question Number 71196 by Rio Michael last updated on 12/Oct/19 $${the}\:{curve}\:{y}\:=\:{f}\left({x}\right),\:{when}\:{f}\left({x}\right)\:{is}\:{a}\:{quadratic}\:{expression}\:{has}\: \\ $$$${a}\:{maximum}\:{value}\:{point}\:{at}\:\left(\mathrm{1},\mathrm{4}\right).\:{The}\:{curve}\:{touches}\:{the}\:{line} \\ $$$$\mathrm{6}{x}\:+\:{y}\:=\:\mathrm{13}.\:{Find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{y}\:=\:\mathrm{8} \\ $$ Answered by MJS last updated on 12/Oct/19 $${f}\left({x}\right)\:\mathrm{is}\:\mathrm{quadratic}\:\Leftrightarrow\:{y}={ax}^{\mathrm{2}}…

find-fhe-range-f-x-4-1-x-

Question Number 71172 by aliesam last updated on 12/Oct/19 $${find}\:{fhe}\:{range} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{1}+\sqrt{{x}}} \\ $$ Commented by kaivan.ahmadi last updated on 12/Oct/19 $$\sqrt{{x}}\geqslant\mathrm{0}\Rightarrow\mathrm{1}+\sqrt{{x}}\geqslant\mathrm{1}\Rightarrow\frac{\mathrm{4}}{\mathrm{1}+\sqrt{{x}}}\leqslant\mathrm{4} \\…