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Chapter 1: Q. 24 (page 88)

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

limx鈫�5鈭�鈥�f(x)=3andlimx鈫�5+鈥�f(x)=1

Short Answer

Expert verified

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

limx鈫�5鈭�鈥�f(x)=3andlimx鈫�5+鈥�f(x)=1

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鈫�5鈭�鈥�f(x)=3andlimx鈫�5+鈥�f(x)=1

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 limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�3(x2-2x-3)=0;youmayassume未鈮�1

For each functionf graphed in Exercises23鈥�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.

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

limx鈫�-1x.

In Exercises 39鈥�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)=x2,ifx<24,ifx=22x+1,ifx>2.

Write each of the inequalities in interval notation:

fx-L<鈭�
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