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Category: Relation and Functions

show-that-x-1-x-2-x-n-R-n-k-1-n-x-k-2-n-k-1-n-x-k-2-a-b-gt-0-p-x-x-n-ax-b-0-could-not-have-more-than-3-reals-solutions-

Question Number 106315 by pticantor last updated on 04/Aug/20 showthat(x1,x2,..,xn)Rn$$\left(\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} \right)^{\mathrm{2}} \leqslant\boldsymbol{{n}}\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} ^{\mathrm{2}} \

If-g-x-x-x-and-lim-x-2-f-x-f-2-x-2-ax-b-4-3-find-the-value-of-f-g-1-

Question Number 106309 by bemath last updated on 04/Aug/20 Ifg(x)=x+xandlimx2f(x)f(2)x2+ax+b=43findthevalueof(fg)(1). Answered by bobhans last updated on 05/Aug/20 $$\mathrm{g}\left(\mathrm{x}\right)=\:\mathrm{x}+\sqrt{\mathrm{x}}\:\Rightarrow\mathrm{g}'\left(\mathrm{x}\right)=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}}\:;\:\mathrm{g}'\left(\mathrm{1}\right)=\:\frac{\mathrm{3}}{\mathrm{2}} \