SOLUTION: For the limit lim x → 2 (x3 − 4x + 5) = 5 illustrate the definition by finding the largest possible values of 𝛿 that correspond to 𝜀 = 0.2 and 𝜀 = 0.1. (Round your a

Question 1174065: For the limit
lim x → 2 (x3 − 4x + 5) = 5
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.)
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!

For 𝜀 = 0.2,
We use a graphing calculator to find x when x³-4x+5 = 5+𝜀 = 5+0.2 = 5.2,
which is x = 2.0245463.  So, in that case, the maximum value of |x-2| = 𝛿 = 0.0245.

For 𝜀 = 0.1,
We find x when x³-4x+5 = 5+𝜀 = 5+0.1 = 5.1, which is x = 2.0123847.  So, in that case, 
the maximum value of |x-2| = 𝛿 = 0.0124

Edwin

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