Find the Coefficient Of $x ^ { 3 }$ In the Maclaurin Series For

question 316

Multiple Choice

Find the coefficient of $x ^ { 3 }$ in the Maclaurin series for $f ( x ) = \sin 2 x$ .

• A) \(- \frac { 2 } { 3 }\)
• B) \(- \frac { 4 } { 3 }\)
• C) \(\frac { 4 } { 3 }\)
• D) \(- \frac { 8 } { 3 }\)
• E) \(\frac { 2 } { 3 }\)
• F) \(\frac { 8 } { 3 }\)
• G) \(- \frac { 1 } { 3 }\)
• H) \(\frac { 1 } { 3 }\)

---

Definitions:

Free Stuff

Items or services offered without charge, usually as part of a promotional strategy or as incentives.

Private Good

A type of good that is rivalrous and excludable, meaning its consumption by one individual prevents others from consuming it.

Common Resource

A type of good that provides users with tangible benefits, but which is available to everyone, such as air, water, and fish in the open sea, leading to potential overuse problems.

Common Resource

A natural or man-made resource where one person’s use diminishes other people’s access or enjoyment, but it is difficult to exclude anyone from using it.