23. The graph of the even function y = f(x) consists of 4 line segments, as shown above. Which of the following statements about f is false? (A) lim_{x?0} (f(x) - f(0)) = 0 (B) lim_{x?0} (f(x) - f(0))/x = 0 (C) lim_{x?0} (f(x) - f(-x))/2x = 0 (D) lim_{x?2} (f(x) - f(2))/(x - 2) = 1 (E) lim_{x?3} (f(x) - f(3))/(x - 3) does not exist.
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However, we can analyze each statement: (A) lim (f(x) - f(0)) = 0: This statement is saying that as x approaches 0, the difference between f(x) and f(0) approaches 0. This is typically true for continuous functions at a given point, but without the graph, we Show more…
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