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Chapter 1: Q. 21 (page 87)

Sketch the graphs of functions that have the given limits and values. (There are multiple correct answers.)

limx→−∞ f(x)=3andlimx→∞ f(x)=−∞

Short Answer

Expert verified

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

limx→−∞ f(x)=3andlimx→∞ f(x)=−∞

We have to sketch the graph of this function.

Step by step solution

01

Step 1. Given information. 

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

limx→−∞ f(x)=3andlimx→∞ f(x)=−∞

We have to sketch the graph of this function.

02

Step 2. Graph the function

The graph is :

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Most popular questions from this chapter

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

Write each of the inequalities in interval notation:

0<|x-2|<0.1

Calculate each of the limits:

limh→0(-1+h)3-(-1)3h.

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

f(x)=x−2

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx→-5x.
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