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Chapter 1: Q. 4 (page 153)

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive

limx鈫�cAxn=?.

Short Answer

Expert verified

The value isAck.

Step by step solution

01

Step 1. Given Information.

The given limit function islimx鈫�cAxn=?.

02

Step 2. Value of the limit.

Power functions are continuous on their domains. In terms of limits, Ais real and kis rational, then for all values x=cat which xkis defined , we have,

limx鈫�cAxk=Ack

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Most popular questions from this chapter

Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point x=c.

f(x)=2鈭�x,鈥呪赌呪赌呪赌�ifxrationalx2,鈥呪赌呪赌呪赌�ifxirrational,c=2

limx鈫�02xex-1

Write each of the inequalities in interval notation:

3x+1-2<0.1

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�2-f(x)=-鈭�,limx鈫�2+f(x)=鈭�,f(2)=3.

What are punctured intervals, and why do we need to use them when discussing limits?
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