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Chapter 1: Q. 9 (page 153)

Consider the limit expression

limx鈫�0+lnxx

Calculate the limit.

Short Answer

Expert verified

The limit of the expression is 1.

Step by step solution

01

Step 1. Given 

The given limit expression islimx鈫�0+lnxx.

02

Step 2. Calculation

From definition we have

limx鈫�0lnxx=1

The evaluation of the following limit is

limx鈫�0lnxx=1

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Most popular questions from this chapter

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

limx鈫�2+32x-4=0

Write each of the inequalities in interval notation:

x2-1+3<0.5

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

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)=2,limx鈫�2+f(x)=1,f(2)=1.

Write each of the inequalities in interval notation:

fx-L<鈭�
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