Find the Taylor Polynomial of Order 3 Generated by F $$f ( x ) = e ^ { - 6 x } , a = 0$$

question 29

Multiple Choice

Find the Taylor polynomial of order 3 generated by f at a.
- $$f ( x ) = e ^ { - 6 x } , a = 0$$

• A) \(P _ { 3 } ( x ) = 1 - 36 x + \frac { 1296 x ^ { 2 } } { 2 } - \frac { 46,656 x ^ { 3 } } { 12 }\)
• B) \(P _ { 3 } ( x ) = 1 - 6 x + \frac { 36 x ^ { 2 } } { 2 } - \frac { 216 x ^ { 3 } } { 6 }\)
• C) \(P _ { 3 } ( x ) = 1 - 6 x + \frac { 36 x ^ { 2 } } { 2 } - \frac { 216 x ^ { 3 } } { 3 }\)
• D) \(P _ { 3 } ( x ) = 1 - 6 x + \frac { 36 x ^ { 2 } } { 2 } - \frac { 216 x ^ { 3 } } { 18 }\)

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Definitions:

Nerve impulses

Electrical signals that travel along the nerve fibers, responsible for transmitting information throughout the body.

Neuroglial cells

Supportive cells in the nervous system that do not conduct electrical impulses but provide support, insulation, and nutrients to neurons.

Axon diameter

The thickness of the axon, a part of a neuron that carries electrical impulses away from the neuron's cell body, which can affect the speed of neural transmission.

Impulse conduction

The process by which electrical signals are transmitted along nerve fibers or muscle fibers.