Which of the Following Is the Degree 2 Taylor Polynomial $a = 3$

question 170

Multiple Choice

Which of the following is the degree 2 Taylor polynomial centered at $a = 3$ for $f ( x ) = \ln x$ ?
1) $\ln 3 + \frac { x - 3 } { 3 } - \frac { ( x - 3 ) ^ { 2 } } { 18 }$ 2) $\ln 3 + \frac { x - 3 } { 3 } - \frac { ( x - 3 ) ^ { 2 } } { 9 }$ 3) $\ln 3 - \frac { x - 3 } { 3 } + \frac { ( x - 3 ) ^ { 2 } } { 18 }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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Definitions:

Protein Synthesis

The process by which cells build proteins based on the instructions encoded in DNA, involving transcription and translation.

mRNA

Messenger RNA, a type of RNA that conveys genetic information from DNA to the ribosome, where it specifies the amino acid sequence of the protein products of gene expression.

DNA

DNA, a molecule responsible for carrying the genetic blueprints essential for the growth, development, operational processes, and reproduction of all recognized living entities and numerous viruses.

Flagellum

A flagellum is a whip-like appendage found on some cells, including bacteria and spermatozoa, that aids in locomotion.