Use the given graph to find 𝛿

Question

Use the given graph of f(x) = sqrt(x) to find the largest number  𝛿 such that

if 0 < | x-9 | < 𝛿 then | sqrt(x) - 3 | < 0.2

Answer 1

I√x -3I < 0.2; - 0.2 < √x - 3 < 0.2; 2.8 < √x < 3.2; 7.84 < x < 10.24; - 1.16 < x - 9 < 1.24.

From here - 1.24 < x - 9 < 1.24; so, Ix - 9I < 1.24. So, δ = 1.24