MULTIPLE CHOICE $x$ Find the Value of the Exact Solution At the Statement

question 43

Multiple Choice

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use Euler's method with the specified step size to estimate the value of the solution at the given point $x$ . Find the value of the exact solution at $x ^ { * }$ .
- $$\mathrm { y } ^ { \prime } = 4 \mathrm { xe } ^ { \mathrm { x } ^ { 4 } } , \mathrm { y } ( 0 ) = 4 , \mathrm { dx } = 0.1 , \mathrm { x } ^ { * } = 1$$

• A) Euler's method gives \(\mathrm { y } \approx 5.7183\); the exact solution is \(6.2619\)
• B) Euler's method gives \(\mathrm { y } \approx 7.0655\); the exact solution is \(5.9901\)
• C) Euler's method gives \(\mathrm { y } \approx 6.4232\); the exact solution is \(5.7183\)
• D) Euler's method gives \(\mathrm { y } \approx 5.7808\); the exact solution is \(5.4465\)

---

Definitions:

Retirement Years

A period in an individual's life post-employment years, often characterized by adjustment to new lifestyles and opportunities for leisure and personal pursuits.

Motor Development

The progression of muscle coordination and strength in children, allowing them to perform more complex physical activities over time.

Cognitive Deficit

Impairment in mental processing abilities such as memory, attention, problem-solving, and decision-making.

Normal Aging

The natural and gradual changes in physical, cognitive, and social abilities that occur as part of the aging process.