The First Four Terms in the Power Series Expansion of the Function

question 24

Multiple Choice

The first four terms in the power series expansion of the function $f ( x ) = e ^ { 2 x }$ about $x = 0$ are

• A) \(1 + x + x ^ { 2 } + x ^ { 3 }\)
• B) \(1 + 2 x + 2 x ^ { 2 } + 2 x ^ { 3 }\)
• C) \(1 + 2 x + 2 x ^ { 2 } + 4 x ^ { 3 } / 3\)
• D) \(1 + 2 x + 2 x ^ { 2 } + 2 x ^ { 3 } / 3\)
• E) \(1 + 2 x + 4 x ^ { 2 } + 8 x ^ { 3 }\)

---

Definitions:

Shredded

Torn or cut into thin pieces typically to prepare or dispose of materials and can also refer to food processing.

Surfacing

The process of appearing or becoming visible, often used in the context of objects coming to the surface of water or information becoming known.

Public Roads

Roads maintained by the government and accessible to the public for transportation purposes, including highways, city streets, and bridges.

Pre-Consumer Waste

Materials discarded during the manufacturing process before the product reaches the consumer, such as scrap material or trimmings.