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Chapter 1: Q. 16 (page 87)

Sketch a function that has the following table of values, but whose limit as $x \to \infty$ is equal to $- \infty$ :

Short Answer

Expert verified

The graph is :

Step by step solution

Step 1. Given information.

We have been given a table of values:

Also, limit as $x \to \infty$ is equal to $- \infty$ .

We have to sketch this function.

Step 2. Sketch the graph

The graph is :

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Most popular questions from this chapter

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.

$\lim_{x \to 1^{-}} \frac{1}{1 - x} = \infty$ , find $δ$ in terms of $M$ .

Calculate each of the limits:

$\lim_{h \to 0} \frac{{(- 1 + h)}^{3} - {(- 1)}^{3}}{h}$ .

For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .

$\lim_{x \to 3} (x^{2} - 6 x + 5) = - 4$

Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.

f is left continuous at x = 1 and right continuous at x = 1, but is not continuous at x = 1, and f(1) = −2.

Write a delta–epsilon proof that proves that f is continuous on its domain. In each case, you will need to assume that δ is less than or equal to 1.

$f (x) = x^{- 1}$

See all solutions

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Sketch a function that has the following table of values, but whose limit as x→∞is equal to -∞:

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Sketch the graph

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Most popular questions from this chapter

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Sketch a function that has the following table of values, but whose limit as $x \to \infty$ is equal to $- \infty$ :