Let SC R² be a compact Jordan measurable set and f: S→ [0, ∞) be continuous. Consider the set A = {(x, y, z) = R³ : (x, y) = S, 0 ≤ z ≤ f(x, y)} Which one of the following inequalities is TRUE? O vol (4) max f(x, y) (x,y)=S vol (A) ≤ vol (S) vol (A) ≤ max f(x, y). vol (S) (x,y)=S None of the above inequalities are generally true.

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A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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A: Since you have put a multipart question, as per company policy, we shall answer only the first part.…