Use Multiplication or Division of Power Series to Find the First

question 45

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) \(5 \left( 1 - 17 x ^ { 2 } + \frac { 67 } { 6 } x ^ { 4 } \right)\)

---

Definitions:

Contraceptive Methods

Various techniques or devices used to prevent pregnancy as a result of sexual intercourse.

Failure Rate

The frequency at which a system, component, or process fails to perform its intended function.

Contraception

Methods or devices used to prevent pregnancy and control fertility, including hormonal pills, barriers, and surgical procedures.

Contraceptive Method

Practices, devices, or medications used to prevent pregnancy as a result of sexual intercourse.