3. (a) Use the Fundamental Theorem of Calculus to determine a continuous function f: 2. x) -R that satisfies tf(t) dt = 3.r² –. sin? r - 12 + sin? 2 for all r> 2. Verify that your answer is correct by computing the integral tf(t) dt once you have deter- mined the function f. (b) Let 0< c

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A: We have given function;

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A: We will solve the question number 2.16 as mentioned. Given that S1,S2 are two convex sets in ℝn+m.…

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A: Let I=∫0bfxfx+fb-xdx   I=∫0bfxfx+fb-xdx                     ....... (1) use ∫0afxdx=∫0afa-xdx…

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A: As per guidelines, I can answer only three subparts.

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Q: c. Let f be differentiable on R. Suppose that f'(x) # 0 for every r. Prove that f has at most one…

A: We can explain this statement by 2 explainations given below

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A: Let A ⊆ R , let f:A → R and let c ∈ A. We say that f is continuous at c if, given any number ε&gt;0,…

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A: We will use greens theorem and properties of an analytic function.