4. Suppose that fis continuous on [a, b] and f(a) < k < f(b). (a) Show that the proof of the IVT generates the largest c e [a, b] for which f(c) = k. (b) How could the set {x E [a, b] | f(x) > k} be used to find the smallest c e [a, b] for which f(c) = k? %3D

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A: Use the Intermediate Value Theorem (IVT) and method of contradicts.

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A:

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A:

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A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

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Q: (a) Show (a, b) ∼ R for any interval (a, b). (b) Show that an unbounded interval like (a,∞) = {x : x…

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A:

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.