Question Number 114709 by mohammad17 last updated on 20/Sep/20
Commented by mohammad17 last updated on 20/Sep/20
$${help}\:{me}\:{sir}\:{pleas} \\ $$
Answered by 1549442205PVT last updated on 20/Sep/20
$$\left.\mathrm{Choose}\:\mathrm{a},\mathrm{b},\mathrm{d},\mathrm{e}\right)\mathrm{80},\mathrm{70},\mathrm{60},\mathrm{50} \\ $$$$\mathrm{We}\:\mathrm{need}\:\mathrm{find}\:\delta\:\mathrm{such}\:\mathrm{that} \\ $$$$\forall\mathrm{x}:\:\:\mid\mathrm{x}−\mathrm{1}\mid<\delta\:\mathrm{then}\:\mid\sqrt{\mathrm{x}}−\mathrm{1}\mid<\mathrm{8}\left(\mathrm{1}\right) \\ $$$$\mathrm{because}\:\mid\sqrt{\mathrm{x}}−\mathrm{1}\mid<\mathrm{8}\Leftrightarrow−\mathrm{8}<\sqrt{\mathrm{x}}−\mathrm{1}<\mathrm{8} \\ $$$$\Leftarrow\mathrm{0}\leqslant\sqrt{\mathrm{x}}<\mathrm{9}\Leftarrow\mathrm{0}\leqslant\mathrm{x}<\mathrm{81}\Leftarrow−\mathrm{1}\leqslant\mathrm{x}−\mathrm{1}<\mathrm{80} \\ $$$$\Leftarrow\mid\mathrm{x}−\mathrm{1}\mid<\mathrm{80} \\ $$$$\mathrm{Hence}\:\mathrm{choose}\:\delta\leqslant\mathrm{80}\:\mathrm{then}\left(\mathrm{1}\right)\:\mathrm{is}\:\mathrm{satisfied} \\ $$
Commented by mohammad17 last updated on 20/Sep/20
$${thank}\:{you}\:{sir}\:{can}\:{you}\:{help}\:{me}\:{in}\:{otber}\:{question} \\ $$