Apply the precise definition of limit to show that, limit as x approaches 4 of (2x+3)=11 , limit as x approaches 4 of (x^(2) -4x+5)=1

Answer 1

Let ε>0 be given, if |x-4|<δ=ε/2, then |2x+3-11|<ε.

The 2nd limit is not correct.

Answer 2

Given ε > 0, let δ = ε/2.

If 0 < l x - 4 l < δ = ε/2, then l (2x + 3) - 11 l = l 2x - 8 l = 2 l x - 4 l < 2(δ) = 2(ε/2) = ε