Find the First Four Nonzero Terms in the Maclaurin Series $x - \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 30 } x ^ { 5 } - \frac { 2 } { 315 } x ^ { 7 } + \ldots$

question 380

Multiple Choice

Find the first four nonzero terms in the Maclaurin series for the function.
-sin x cos x

• A) \(x - \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 30 } x ^ { 5 } - \frac { 2 } { 315 } x ^ { 7 } + \ldots\)
• B) \(x - \frac { 2 } { 3 } x ^ { 3 } + \frac { 2 } { 15 } x ^ { 5 } - \frac { 4 } { 315 } x ^ { 7 } + \ldots\)
• C) \(1 + x - \frac { 1 } { 2 } x ^ { 2 } - \frac { 1 } { 6 } x ^ { 3 } + \ldots\)
• D) \(x + \frac { 1 } { 3 } x ^ { 3 } - \frac { 2 } { 15 } x ^ { 5 } + \frac { 4 } { 315 } x ^ { 7 } + \ldots\)

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Definitions:

Lauric Acid

A saturated fatty acid with a 12-carbon chain commonly found in coconut oil and palm kernel oil.

Triglyceride

A type of fat (or lipid) that is found in the blood, composed of one molecule of glycerol bonded to three fatty acids.

Melting Point

The temperature at which a substance changes from a solid to a liquid at atmospheric pressure.

Linoleic Acid

An essential polyunsaturated fatty acid found in many vegetable oils, important for the structure and function of cellular membranes.