Question

Asked Mar 24, 2019

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Find the largest number *δ* such that if |*x* − 4| < *δ*, then |2*x* − 8| < *ε*, where *ε* = 0.1.*δ* ≤ 1

Repeat and determine *δ* with *ε* = 0.01.*δ* ≤ 2

Step 1

When ε=0.1 and δ≤1

Simplifying the absolute value inequality:

Step 2

Checking the minimum and maximum values of *x* in the required inequality:

Hence, 0.05<δ≤1

Therefore, the largest value of δ is 1

Step 3

When ε=0.01 and δ≤2

Simplify...

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