Find the Taylor Polynomial of Order 3 Generated by F $$f ( x ) = \ln ( x + 1 ) , a = 6$$

question 202

Multiple Choice

Find the Taylor polynomial of order 3 generated by f at a.
- $$f ( x ) = \ln ( x + 1 ) , a = 6$$

• A) \(P _ { 3 } ( x ) = \ln 5 + \frac { x - 6 } { 5 } + \frac { ( x - 6 ) ^ { 2 } } { 50 } + \frac { ( x - 6 ) ^ { 3 } } { 375 }\)
• B) \(P _ { 3 } ( x ) = \ln 7 - \frac { x - 6 } { 7 } + \frac { ( x - 6 ) ^ { 2 } } { 98 } - \frac { ( x - 6 ) ^ { 3 } } { 1029 }\)
• C) \(P _ { 3 } ( x ) = \ln 5 - \frac { x - 6 } { 5 } + \frac { ( x - 6 ) ^ { 2 } } { 50 } - \frac { ( x - 6 ) ^ { 3 } } { 375 }\)
• D) \(\mathrm { P } _ { 3 } ( \mathrm { x } ) = \ln 7 + \frac { \mathrm { x } - 6 } { 7 } - \frac { ( \mathrm { x } - 6 ) ^ { 2 } } { 98 } + \frac { ( \mathrm { x } - 6 ) ^ { 3 } } { 1029 }\)

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Definitions:

Metabolic Activity

The set of life-sustaining chemical reactions in organisms, including digestion and the transport of substances into and between different cells.

Distal Tubule

A portion of kidney nephron between the loop of Henle and collecting duct system that plays a crucial role in the reabsorption of water, sodium, and calcium and in the secretion of potassium and hydrogen ions.

Ureter

One of two tubes that carries urine from a kidney to the bladder.