Find a number 𝛿

Question

Find a number 𝛿 such that lim_𝑥→2 1/x = 1/2 is accurate for 𝜀 to equal 0.2

Answer 1

You need to solve 2 equations:

(1/x)-(1/2)<1/5 and -(1/x)+(1/2<1/5

The solutions will give you 2 possible values for δ and you need to pick the one which will satisfy BOTH equations.

I believe that you did not solve the equations correctly; the solutions are x>10/7 and x<10/3.

The one closer to 2 is the one which will work for both...that is δ=4/3, i.e.

|x-2|<4/3.