Solve the Problem Can Be Used to Estimate the Value Of

question 138

Multiple Choice

Solve the problem.
-The series $\ln ( \mathrm { x } ) = ( \mathrm { x } - 1 ) - \frac { ( \mathrm { x } - 1 ) ^ { 2 } } { 2 } + \frac { ( \mathrm { x } - 1 ) ^ { 3 } } { 3 } - \ldots + ( - 1 ) ^ { \mathrm { n } - 1 } \frac { ( \mathrm { x } - 1 ) ^ { \mathrm { n } } } { \mathrm { n } }$ can be used to estimate the value of $\ln ( a )$ for any positive real number a such that $0 < a \leq 2$ . Use the first five terms of this series to estimate $\ln ( 1.54 )$ . Round to the nearest thousandth.

• A) \(- 0.495\)
• B) \(0.435\)
• C) \(1.995\)
• D) \(1.325\)

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Definitions:

Conservation

In cognitive development, the understanding that certain properties of objects can remain the same despite changes in their form or appearance.

Cognitive Ability

The capacity of an individual to perform the various mental activities most closely associated with learning and problem solving.

Volume or Mass

The volume refers to the amount of space an object occupies, while mass is a measure of an object's quantity of matter.

Piagetian Thought

A theory of cognitive development proposed by Jean Piaget, detailing how children construct a mental model of the world through stages.