Use the graph of f(x)=x2 below to find a number δ such that ∣∣x2−1∣∣<0.1 whenever 0<|x−1|<δ .

Question

Answer 1

|x²-1|<0.1

-0.1 < x²-1 < 0.1

0.9 < x² < 1.1

√(0.9) < x < √(1.1)

√(0.9) - 1 < x-1 < √(1.1) - 1

-0.0513 < x-1 < 0.0488

Since δ>0, then 0 < |x-1| < 0.0488

Therefore, δ = 0.0488

Hope this helped!