Provide an Appropriate Response $\ln 2 = \infty - \infty$ Where Does the Argument Go Wrong

question 155

Essay

Provide an appropriate response.
-Here is an argument that $\ln 2 = \infty - \infty$ . Where does the argument go wrong?
$\ln 2 = \ln 1 + \ln 2 = \ln 1 - \ln \frac { 1 } { 2 }$
$= \lim _ { b \rightarrow \infty } \ln \left( \frac { b - 1 } { b } \right) - \ln \frac { 1 } { 2 }$ $= \lim _ { b \rightarrow \infty } \left[ \ln \frac { x - 1 } { x } \right] _ { 2 } ^ { b }$
$= \lim _ { b \rightarrow \infty } [ \ln ( x - 1 ) - \ln x ] _ { 2 } ^ { b }$
$= \lim _ { b \rightarrow \infty } \int _ { 2 } ^ { b } \left( \frac { 1 } { x - 1 } - \frac { 1 } { x } \right) d x$
$= \int _ { 2 } ^ { \infty } \left( \frac { 1 } { x - 1 } - \frac { 1 } { x } \right) d x$
Here is an argument that $\ln 2 = \infty - \infty .$
$\ln 2 = \ln 1 + \ln 2 = \ln 1 - \ln \frac { 1 } { 2 }$
$= \lim _ { b \rightarrow \infty } \ln \left( \frac { b - 1 } { b } \right) - \ln \frac { 1 } { 2 }$
$= \lim _ { b \rightarrow \infty } \left[ \ln \frac { x - 1 } { x } \right] _ { 2 } ^ { b }$
$= \lim _ { b \rightarrow \infty } [ \ln ( x - 1 ) - \ln x ] { } _ { 2 } ^ { b }$
$= \lim _ { b \rightarrow \infty } \int _ { 2 } ^ { b } \left( \frac { 1 } { x - 1 } - \frac { 1 } { x } \right) d x$
$= \int _ { 2 } ^ { \infty } \left( \frac { 1 } { x - 1 } - \frac { 1 } { x } \right) d x$
$= \int _ { 2 } ^ { \infty } \frac { 1 } { x - 1 } d x - \int _ { 2 } ^ { \infty } \frac { 1 } { x } d x$
$= \lim _ { b \rightarrow \infty } [ \ln ( x - 1 ) ] \frac { b } { b } - \lim [ \ln x ]$
$= \infty - \infty$
$= \int _ { 2 } ^ { \infty } \frac { 1 } { x - 1 } d x - \int _ { 2 } ^ { \infty } \frac { 1 } { x } d x$
$= \lim _ { b \rightarrow \infty } [ \ln ( x - 1 ) ] _ { 2 } ^ { b } - \lim _ { b \rightarrow \infty } [ \ln x ] _ { 2 } ^ { b }$
$= \infty - \infty$

Understand the basics of social computing platforms and their features for user engagement and e-commerce.

Understand how to calculate and interpret the current ratio to assess a company's short-term liquidity.

Analyze a company's operating performance through net operating income, net income, and earnings per share calculations.

Calculate and understand dividend ratios, including dividend yield and dividend payout ratios, to evaluate a company's dividend policy.

---

Definitions:

Unflattering Information

Negative or disadvantageous facts or news about a person or organization that may affect perceptions or decisions unfavorably.

Prospect Pool

A group of potential customers or clients who might be interested in a company's product or service.

Salespeople

Individuals who sell products or services, aiming to meet customer needs and achieve sales targets.

CRM Technology

CRM Technology refers to Customer Relationship Management software that helps businesses manage interactions with current and potential customers, streamlining processes and improving relationships.