Question-158341

Question Number 158341 by aliibrahim1 last updated on 02/Nov/21

Answered by puissant last updated on 03/Nov/21

T h a t i s ε > 0, {l e t}^{'} s s e e k α > 0 / \forall x \in R, 0 <∣ x - 2 ∣< α \Rightarrow ∣ x^{2} - 4 ∣< ε

f o r x \in R, ∣ x^{2} - 4 ∣ = ∣ x - 2 ∣ . ∣ x + 2 ∣ w e h a v e ∣ x - 2 ∣< 2 \to 0 < x + 2 < 6

\Rightarrow ∣ x^{2} - 4 ∣< 6 ∣ x - 2 ∣; ∣ x^{2} - 4 ∣< ε \to 6 ∣ x - 2 ∣< ε \to ∣ x - 2 ∣< \frac{ε}{6}

t a k e α = m i n (2; \frac{ε}{6}) \dots .

\dots \dots \dots \dots \dots . . L e p u i s s a n t \dots \dots \dots \dots \dots

Commented by aliibrahim1 last updated on 04/Nov/21

t h x s i r