For each function f graphed in Exercises 23–26, describe the intervals on which f is continuous. For each discontinuity of f, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.
The graph is continuous on the interval and it has a jump discontinuity and the function is right continuous at
The given graph is
From the graph, we can depict that graph is continuous on the interval
From the graph, we can depict that it has a jump discontinuity. The function is right continuous at
Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) A limit exists if there is some real number that it is equal to.
(b) The limit of as is the value .
(c) The limit of as might exist even if the value of does not.
(d) The two-sided limit of as exists if and only if the left and right limits of exists as .
(e) If the graph of has a vertical asymptote at , then .
(f) If , then the graph of has a vertical asymptote at .
(g) If , then the graph of has a horizontal asymptote at .
(h) If , then the graph of has a horizontal asymptote at .
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