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:

Corpus Callosum

A large band of neural fibers connecting the two hemispheres of the brain, facilitating interhemispherical communication.

Split Brains

A condition that results from severing the corpus callosum, leading to a disconnection syndrome where the two hemispheres of the brain cannot exchange information directly.

Brain Plasticity

The brain's ability to change and adapt as a result of experience, by reorganizing and forming new neural connections.

Corpus Callosum

A wide band of nerve fibers connecting the left and right hemispheres of the brain, facilitating interhemispheric communication.