Use Multiplication or Division of Power Series to Find the First

question 80

Multiple Choice

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.
$$f ( x ) = 5 e ^ { - x ^ { 2 } } \cos 4 x$$

• A) \(5 \left( 1 - 17 x ^ { 2 } + \frac { 115 } { 6 } x ^ { 4 } \right)\)
• B) \(5 \left( 1 - 9 x ^ { 2 } + \frac { 115 } { 6 } x ^ { 4 } \right)\)
• C) \(5 \left( 1 - 9 x + \frac { 115 } { 6 } x ^ { 4 } \right)\)
• D) \(5 \left( 1 - 9 x ^ { 2 } + \frac { 97 } { 6 } x ^ { 4 } \right)\)
• E) \(5 \left( 1 - 17 x ^ { 2 } + \frac { 67 } { 6 } x ^ { 4 } \right)\)

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Definitions:

Midbrain

A part of the brainstem that plays a crucial role in motor movement, particularly movements of the eye, and in auditory and visual processing.

Hindbrain

The posterior part of the brain that includes the cerebellum, pons, and medulla oblongata, involved in regulating basic life functions.

Forebrain

The anterior part of the brain, including the cerebral hemispheres, thalamus, and hypothalamus, responsible for cognitive, sensory, and motor functions, and emotion and memory processing.

Thalamus

A major part of the vertebrate brain, serving as a principal hub for relaying sensory information to the cerebral cortex.