Each of the following statements is false. For each statement, sketchthe graph of a function that provides a counterexample.(a) If lim f(x) exists, then f is continuous atx = a. a x→ a(b) If f has a jump discontinuity at x = a, then f(a) is equal to eitherlim f(x) or lim f(x). x→ a- x→ a+
Each of the following statements is false. For each statement, sketchthe graph of a function that provides a counterexample.(a) If lim f(x) exists, then f is continuous atx = a. a x→ a(b) If f has a jump discontinuity at x = a, then f(a) is equal to eitherlim f(x) or lim f(x). x→ a- x→ a+
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Each of the following statements is false. For each statement, sketch
the graph of a function that provides a counterexample.
(a) If lim f(x) exists, then f is continuous atx = a. a
x→ a
(b) If f has a jump discontinuity at x = a, then f(a) is equal to either
lim f(x) or lim f(x).
x→ a- x→ a+
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