a. Show that Theorem 2.2 is true if the inequality |g'(x)|k is replaced by g'(x) k,
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b. Show that Theorem 2.3 may not hold if inequality |g'(x)| ≤ k is replaced by g'(x) ≤ k. [Show that g(x) = 1 − x2, for x in [0, 1], provides a counterexample.]
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