Question-80220

Question Number 80220 by TawaTawa last updated on 01/Feb/20

Commented by kaivan.ahmadi last updated on 01/Feb/20

\forall ϵ > 0 \exists δ > 0 s . t ∣ x - 3 ∣< δ \Rightarrow∣ x^{2} - 9 ∣< ϵ

∣ x^{2} - 9 ∣=∣ x - 3 ∣∣ x + 3 ∣< ϵ

i f δ = 1 \Rightarrow∣ x - 3 ∣< 1 \Rightarrow - 1 < x - 3 < 1 \Rightarrow 2 < x < 4 \Rightarrow

5 < x + 3 < 7 \Rightarrow∣ x + 3 ∣< 7

n o w

∣ x - 3 ∣< \frac{ϵ}{7}

i f ϵ = 0.01 \Rightarrow δ < \frac{0.01}{7} = \frac{1}{700}

i f ϵ = 0.00001 \Rightarrow δ < \frac{1}{70000}

Commented by TawaTawa last updated on 01/Feb/20

God bless you sir

Commented by TawaTawa last updated on 01/Feb/20

How did you come across 5 and 7 sir