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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}…

Given-function-f-x-2x-2-1-x-lt-3-5x-1-x-3-Find-out-f-x-2-7-A-5x-2-34-B-2x-2-8-C-5x-2-36-D-5x-2-34-E-2-x-2-7-2-1-Please-help-

Question Number 116776 by abony1303 last updated on 06/Oct/20 $$\mathrm{Given}\:\mathrm{function}: \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1},\:\:\mid{x}\mid<\mathrm{3}}\\{\mathrm{5x}−\mathrm{1},\:\:\mid{x}\mid\geqslant\mathrm{3}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{out}:\:{f}\left({x}^{\mathrm{2}} +\mathrm{7}\right)=? \\ $$$$ \\ $$$$\left.\mathrm{A}\left.\right)\left.\mathrm{5x}^{\mathrm{2}} −\mathrm{34}\:\:\:\:\:\mathrm{B}\right)\mathrm{2x}^{\mathrm{2}} +\mathrm{8}\:\:\:\mathrm{C}\right)\mathrm{5x}^{\mathrm{2}} +\mathrm{36} \\ $$$$\left.\mathrm{D}\left.\right)\mathrm{5x}^{\mathrm{2}}…

Question-182298

Question Number 182298 by SEKRET last updated on 07/Dec/22 Answered by mr W last updated on 07/Dec/22 $${radius}:\:{r} \\ $$$${center}:\:\left({k},\mathrm{2}−{r}\right) \\ $$$${touching}\:{point}\:{with}\:{y}={x}^{\mathrm{2}} :\:\left({p},{p}^{\mathrm{2}} \right) \\…