Given the Vector-Valued Function Below, Evaluate $$\mathbf { r } ( 11 + \Delta t ) - \mathbf { r } ( 11 )$$

question 18

Multiple Choice

Given the vector-valued function below, evaluate $$\mathbf { r } ( 11 + \Delta t ) - \mathbf { r } ( 11 )$$ $$\mathbf { r } ( t ) = \ln t \mathbf { i } + \frac { 8 } { t } \mathbf { j } + 4 t \mathbf { k }$$

• A) \(\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \mathbf { k }\)
• B) \(\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } + \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \Delta t \mathbf { k }\)
• C) \(\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \Delta t \mathbf { k }\)
• D) \(\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) } \mathbf { j } + 4 \Delta t \mathbf { k }\)
• E) \(\ln \left( 1 - \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \Delta t \mathbf { k }\)

---

Definitions:

Production Data

Refers to information generated during the manufacturing or production process of a company, detailing aspects like quantity manufactured, defects, and production time.

Sales Data

Information regarding the quantity of goods or services sold within a specific period, often used for analysis in business strategies.

Scenario Manager

A feature found in some software applications, such as Microsoft Excel, that allows users to create and analyze different scenarios by changing a set of values.

Data Table

A structured arrangement of data organized in rows and columns for easy analysis and manipulation.