Some Applications of Calculus Use a Mathematical Structure Called a Power

question 290

Multiple Choice

Some applications of calculus use a mathematical structure called a power series. To find the interval of convergence of a power series, it is often necessary to solve an absolute value inequality. Solve the absolute value inequality below to find the interval of convergence
- $$\left| \frac { x + 1 } { 4 } \right| < 1$$

• A) \([ 0,3 ]\)
• B) \(( - 5,3 )\)
• C) \([ - 5,3 ]\)
• D) \(( 0,3 )\)

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Definitions:

Carboxyl Group

A functional group consisting of a carbon atom double-bonded to an oxygen atom and single-bonded to a hydroxyl group, denoted as -COOH in organic compounds.

Prostaglandins

A group of physiologically active lipid compounds having diverse hormone-like effects in animals, derived enzymatically from fatty acids.

Arachadonic Acid

A polyunsaturated omega-6 fatty acid important in the inflammation process and cellular signalling.

Chair Conformation

A stable, puckered conformation of six-membered rings that minimizes torsional strain.