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Answer :
The question is about determining a delta value in the epsilon-delta limit definition using the function f(x) = 3x - 1. Based on f(x), as x approaches 4 the value is 11 setting up |f(x) - 11| < ε. After transforming equations, we can conclude that δ = ε/3.
The question seems to involve the epsilon-delta definition of a limit in calculus. Specifically, it appears to be learning about the limit of the function f(x) = 3x - 1 as x approaches 4.
To use the epsilon-delta definition, we wish to find a delta (δ) such that 0 < |x - 4| < δ implies |f(x) - 11| < ε. The value 11 comes from substituting 4 (which is the limit point) into the function, giving us 3(4)-1=11.
To find the exact value of δ, we have to adjust the equation |f(x) - 11| < ε into an equivalent form of 0 < |x - 4| < δ. Doing so, we find that |3x - 12| < ε or 3|x - 4| < ε. Divide through by 3 to find |x - 4| < ε/3, therfore δ = ε/3 would satisfy the condition.
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