Find the First Four Terms of the Binomial Series for the Given

question 264

Multiple Choice

Find the first four terms of the binomial series for the given function.
- $$( 1 + 5 x ) ^ { 1 / 3 }$$

• A) \(1 + \frac { 5 } { 3 } x - \frac { 25 } { 9 } x ^ { 2 } + \frac { 625 } { 81 } x ^ { 3 }\)
• B) \(1 + \frac { 5 } { 3 } x + \frac { 25 } { 9 } x ^ { 2 } + \frac { 125 } { 27 } x ^ { 3 }\)
• C) \(1 + \frac { 5 } { 3 } x - \frac { 25 } { 9 } x ^ { 2 } + \frac { 125 } { 27 } x ^ { 3 }\)
• D) \(1 - \frac { 5 } { 3 } x + \frac { 25 } { 3 } x ^ { 2 } - \frac { 625 } { 81 } x ^ { 3 }\)

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Definitions:

Somatic Nervous System

The part of the peripheral nervous system that handles voluntary control of body movements through the control of skeletal muscles.

Autonomic Nervous System

Part of the nervous system that controls involuntary body functions, such as heart rate, digestion, and respiration, divided into the sympathetic and parasympathetic nervous systems.

Parasympathetic Nervous System

Part of the autonomic nervous system that conserves energy as it slows the heart rate, increases intestinal and gland activity, and relaxes sphincter muscles.

Insulin

A hormone produced by the pancreas that regulates blood sugar levels by facilitating the uptake of glucose into tissues.