Find the Fourth Degree Taylor Polynomial Centered At $c = 7$

question 162

Multiple Choice

Find the fourth degree Taylor polynomial centered at $c = 7$ for the function. $f ( x ) = \ln x$

• A) \(\ln 7 - \frac { 1 } { 7 } ( x - 7 ) - \frac { 1 } { 98 } ( x - 7 ) ^ { 2 } - \frac { 1 } { 1029 } ( x - 7 ) ^ { 3 } - \frac { 1 } { 9604 } ( x - 7 ) ^ { 4 }\)
• B) \(\ln 7 + 7 ( x - 7 ) - 98 ( x - 7 ) ^ { 2 } + 1029 ( x - 7 ) ^ { 3 } - 9604 ( x - 7 ) ^ { 4 }\)
• C) \(\ln 7 + \frac { 1 } { 7 } ( x - 7 ) - \frac { 1 } { 98 } ( x - 7 ) ^ { 2 } + \frac { 1 } { 1029 } ( x - 7 ) ^ { 3 } - \frac { 1 } { 9604 } ( x - 7 ) ^ { 4 }\)
• D) \(\ln 7 - 7 ( x - 7 ) + 98 ( x - 7 ) ^ { 2 } - 1029 ( x - 7 ) ^ { 3 } + 9604 ( x - 7 ) ^ { 4 }\)
• E) \(\ln 7 - \frac { 1 } { 7 } ( x - 7 ) + \frac { 1 } { 98 } ( x - 7 ) ^ { 2 } - \frac { 1 } { 1029 } ( x - 7 ) ^ { 3 } + \frac { 1 } { 9604 } ( x - 7 ) ^ { 4 }\)

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Definitions:

Undisclosed Principal

A situation in contract law where an agent acts on behalf of a principal, but the identity of the principal is not revealed to the third party.

Personal Liability

An individual's legal responsibility to satisfy debts or obligations from personal assets, not just those tied to a particular venture or entity.

Scope of Authority

The range or extent of power that an individual or organization legally has to perform actions or make decisions.

Negligence

The failure to exercise the care that a reasonably prudent person would exercise in like circumstances.