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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鈫�鈭�鈭�鈥�f(x)=3andlimx鈫�鈭�鈥�f(x)=鈭�鈭�

Short Answer

Expert verified

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

limx鈫�鈭�鈭�鈥�f(x)=3andlimx鈫�鈭�鈥�f(x)=鈭�鈭�

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�鈭�鈭�鈥�f(x)=3andlimx鈫�鈭�鈥�f(x)=鈭�鈭�

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

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�46x-1=23.

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�31x=13;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.

Use what you know about one-sided limits to prove that a function f is continuous at a point x=cif and only if it is both left and right continuous at x=c.

Write delta-epsilon proofs for each of the limit statements in Exercises 47鈥�60.

limx鈫�2+32x-4=0
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