Question

How do you prove that the limit of `(3x+2)=8` as x approaches 2 using the epsilon delta proof?

Answer 1

`delta(epsilon)=epsilon/3`

Explanation:

`abs(f(x)-L)=abs(3x+2-8)=3abs(x-2)`

Then if we choose `delta=epsilon/3`

`abs(x-2) < delta=\ \ =>\ \ abs(f(x)-L)=3abs(x-2)<3delta=epsilon`