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Aug 07, 16Apply the Riemann sum definition of an integral to line integrals as defined by vector fields Now that we are dealing with vector fields, we need to find a way to relate how differential elements of a curve in this field (the unit tangent vectors) interact with the field itselfConversely, assume that f(f−1) = C for all C ⊆ Y but that f is not ontoThen there exists y∈ Y such that for all x∈ X, we have y6= f(x) Let C= {y} Then f−1 = ∅ and f(f−1) = ∅ 6= C since y∈ C ContradictionHence, f is onto Thus, f is onto if and only if f(f−1) = C for all C⊆ Y 8(a) Claim f(A∪B) = f(A) ∪f(B)Y is the output measure, such as process cycle time or customer satisfaction f is the letter representing "function" (what the value(s) of X(s) does/do for Y (the output) X(s) is/are any process input(s) (variables) having assigned or inherent values(s) that is/are involved in



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