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Find-radius-and-center-of-S-S-x-y-z-4-y-2-yz-z-2-4-y-z-

Question Number 182369 by mathocean1 last updated on 08/Dec/22 $${Find}\:{radius}\:{and}\:{center}\:{of}\:\left({S}\right): \\ $$$$\left({S}\right):\begin{cases}{{x}+{y}+{z}=\mathrm{4}}\\{{y}^{\mathrm{2}} +{yz}+{z}^{\mathrm{2}} =\mathrm{4}\left({y}+{z}\right)}\end{cases} \\ $$ Commented by a.lgnaoui last updated on 09/Dec/22 $$\mathrm{y}+\mathrm{z}=\mathrm{4}−\mathrm{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\right) \\…

prove-the-limit-lim-x-2-2x-2-

Question Number 116819 by joki last updated on 07/Oct/20 $${prove}\:{the}\:{limit} \\ $$$${li}\underset{{x}−\rangle\mathrm{2}} {{m}}\sqrt{\mathrm{2}{x}}=\mathrm{2} \\ $$ Answered by 1549442205PVT last updated on 07/Oct/20 $$\mathrm{Suppose}\:\mathrm{0}<\epsilon<\mathrm{2}\:\mathrm{be}\:\mathrm{arbitrary}\:\mathrm{small}\:\mathrm{numer} \\ $$$$\mathrm{so}\:\mathrm{that}\mid\sqrt{\mathrm{2x}}−\mathrm{2}\mid<\epsilon\Leftrightarrow−\epsilon+\mathrm{2}<\sqrt{\mathrm{2x}}<\epsilon+\mathrm{2}…