AP Calculus BC 1.10 Discontinuities Overview

Classify discontinuities and use one-sided limits, two-sided limits and function values to justify whether a function is continuous.

Exam points

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The graph of y=f(x) is shown above. Which of the following is true?

$\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$ exists.

$\lim _{x \rightarrow a^{+}} f(x) \neq \lim _{x \rightarrow a^{-}} f(x)$

$\lim _{x \rightarrow a} f(x) \neq f(a)$

$\lim _{x \rightarrow a} f(x)$ does not exist.

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