Find the Taylor Polynomial of Order 3 Generated by F $$f ( x ) = x ^ { 2 } , a = 5$$

question 280

Multiple Choice

Find the Taylor polynomial of order 3 generated by f at a.
- $$f ( x ) = x ^ { 2 } , a = 5$$

• A) \(P _ { 3 } ( x ) = 1 + 50 ( x - 5 ) + 375 ( x - 5 ) ^ { 2 } + 2500 ( x - 5 ) ^ { 3 }\)
• B) \(\mathrm { P } _ { 3 } ( \mathrm { x } ) = 25 + 10 ( \mathrm { x } - 5 ) + 15 ( \mathrm { x } - 5 ) ^ { 2 } + 20 ( \mathrm { x } - 5 ) ^ { 3 }\)
• C) \(P _ { 3 } ( x ) = 25 + 10 ( x - 5 ) + ( x - 5 ) ^ { 2 }\)
• D) \(P _ { 3 } ( x ) = 1 + 10 ( x - 5 ) + 15 ( x - 5 ) ^ { 2 } + 20 ( x - 5 ) ^ { 3 }\)

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Definitions:

UCR

An unconditioned response, which is an automatic or natural reaction to an unconditioned stimulus without prior conditioning.

Delayed Conditioning

A conditioning process where there is a time gap between the presentation of the conditioned stimulus (CS) and the unconditioned stimulus (US) that leads to learning.

Trace Conditioning

A form of classical conditioning where there is a time interval between the conditioned stimulus and the unconditioned stimulus, requiring the subject to maintain a memory of the CS to form the association.

Cortex

The outermost layer of the brain, responsible for complex cognitive functions, memory, and decision-making.