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Chapter 1: Q. 6 (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�鈭�x-k=?.

Short Answer

Expert verified

The value is0.

Step by step solution

01

Step 1. Given Information.

The given limit function islimx鈫�鈭�x-k.

02

Step 2. Value of the limit.

We know,

Ifk>0,

Then,

limx鈫�鈭�x-k=0

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Most popular questions from this chapter

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)=-x,ifx<02,ifx=0x,ifx>0.

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

f(x)=x鈭�1

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

f is left continuous at x = 2 but not continuous at x = 2, and f(2) = 3.

Calculate each of the limits:

limx鈫�01sec-1x.

Calculate each of limits:

limx鈫�11sin-1x.
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