Limits problem 02.mws

1. Beyond the clause: for every positive epsilon

In the definition of a limit, something must happen for every positive epsilon . Consider the function f(x) = (2*x^2-2*x)/(x-1) . This function simplifies to f(x) = 2*x if x does not equal 1. We have limit(f(x),x = 1) = limit(2*x,x = 1) = 2 .

Submission:

Given an epsilon what delta must be chosen to guarantee that abs(x-1) < delta implies abs(f(x)-2) < epsilon . What we are looking for here is a function delta(epsilon) that tells us how to compute delta given an epsilon . Please explain your answer using complete English sentences.

Submission Worksheet: