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Chapter 1: Q. 23 (page 88)

Sketch the graphs of functions that have the given limits and values. (There are multiple correct answers.)
$lim_{x \to 0^{+}} f (x) = \infty and lim_{x \to 0^{-}} f (x) = \infty$

Short Answer

Expert verified

We have been given the limits and their values for a function:

$lim_{x \to 0^{+}} f (x) = \infty and lim_{x \to 0^{-}} f (x) = \infty$

We have to sketch the graph of this function.

Step by step solution

Step 1. Given information.

We have been given the limits and their values for a function:

$lim_{x \to 0^{+}} f (x) = \infty and lim_{x \to 0^{-}} f (x) = \infty$

We have to sketch the graph of this function.

Step 2. Graph the function

The graph is :

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Most popular questions from this chapter

In Exercises 39–44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

$f (x) = \{\begin{array}{l} (x - 3), i f x < 0 \\ - (x - 3), i f x ⩾ 0 \end{array} .$

Calculate each of the limits:

$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ .

Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes.

For each limit statement in Exercises $41 - 44$ , use algebra to find $δ$ or $N$ in terms of $ε$ or $M$ , according to the appropriate formal limit definition.

$\lim_{x \to \infty} (x^{2} + 2) = \infty$ ,find $N$ in terms of $M$ .

Use algebra to find the largest possible value of δ or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.
$If x > N, then 1 - 2 x < - 500$

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Sketch the graphs of functions that have the given limits and values. (There are multiple correct answers.)limx→0+ f(x)=∞andlimx→0− f(x)=∞

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the function

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Most popular questions from this chapter

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Sketch the graphs of functions that have the given limits and values. (There are multiple correct answers.)
$lim_{x \to 0^{+}} f (x) = \infty and lim_{x \to 0^{-}} f (x) = \infty$