Answer
(a) False.
(b) True.
(c) False.
(d) True.
(e) False.
Work Step by Step
(a) False. The correct statement is: "$f(x)$ is continuous at $x=a$ if the left-and right-hand limits of $f(x)$ as $x \rightarrow a$ exist and equal $f(a)$."
(b) True.
(c) False. The correct statement is: "If the left-and right-hand limits of $f(x)$ as $x \rightarrow a$ are equal but not equal to $f(a)$ then $f$ has a removable discontinuity at $x=a$."
(d) True.
(e) False. The correct statement is: "If $f(x)$ and $g(x)$ are continuous at $x=a$ and $g(a) \neq 0,$ then $f(x) / g(x)$ is continuous."
