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Chapter 3

Continuity

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Problem 1

$ \text {Is the function} f(x)=\left\{\begin{array}{ll}{x+7,} & {x<2} \\ {9, x=2} & {\text { continuous at } x=2 ?} \\ {3 x+3,} & {x>2}\end{array}\right.$

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Problem 2

$ \text {Is the function}f(x)=\left\{\begin{array}{l}{4 x^{2}-2 x, x<3} \\ {10 x-1, x=3 \text { continuous at } x=3 ?} \\ {30, x>3}\end{array}\right.$

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Problem 3

Is the function $f(x)=\sec x$ continuous everywhere?

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Problem 4

Is the function $f(x)=\sec x$ continuous on the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] ?$

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Problem 5

Is the function $f(x)=\sec x$ continuous on the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)?$

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Problem 6

For what value(s) of $k$ is the function $f(x)=\left\{\begin{array}{l}{3 x^{2}-11 x-4, x \leq 4} \\ {k x^{2}-2 x-1, x>4}\end{array} \text { continuous at } x=4 ?\right.$

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Problem 7

At what point is the removable discontinuity for the function $f(x)=\frac{x^{2}+5 x-24}{x^{2}-x-6}?$

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Problem 8

(Graph is not available to copy)

Given the graph of $f(x)$ above, find
(a) $\lim _{x \rightarrow-\infty} f(x)$
(b) $\lim _{x \rightarrow \infty} f(x)$
(c) $\lim _{x \rightarrow 3^{-}} f(x)$
(d) $\lim _{x \rightarrow 3^{+}} f(x)$
(e) $f(3)$
(f) Any discontinuities.

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