For the limit

lim

x → 2

(x^3 − 4x + 7) = 7

illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.)...note:let d=delta, E=epsilon

My work:

0</x-a/<d, then /f(x)-L/<E

0</x-2/<d, then /x^3-4x/<E...

so taking the right part of the statement further:

/x(x^2-4)/<E

/x(x-2)(x+2)/<E

/x-2/< E/(x^2+2x)

d<E/(x^2+2x)

I'm not sure what to do here. Even if I plug in E=0.2, I'm still left with the x's...please help me out, any advice/tips are appreciated.