Use Euler's Method to Calculate the First Three Approximations to the Given

question 67

Multiple Choice

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Round your results to four decimal places.
- $\mathrm { y } ^ { \prime } = 4 x \mathrm { e } ^ { \mathrm { x } ^ { 4 } } , \mathrm { y } ( - 1 ) = 2 , \mathrm { dx } = 0.1$

• A) \(\mathrm { y } 1 = 1.0040 , \mathrm { y } _ { 2 } = 0.3101 , \mathrm { y } _ { 3 } = - 0.1718\)
• B) \(\mathrm { y } _ { 1 } = 0.9127 , \mathrm { y } _ { 2 } = 0.2189 , \mathrm { y } _ { 3 } = - 0.2631\)
• C) \(\mathrm { y } _ { 1 } = 0.7301 , \mathrm { y } _ { 2 } = 0.0363 , \mathrm { y } _ { 3 } = - 0.4457\)
• D) \(\mathrm { y } _ { 1 } = 0.8214 , \mathrm { y } _ { 2 } = 0.1276 , \mathrm { y } _ { 3 } = - 0.3544\)

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Definitions:

Epiphyseal Lines

The remnants of growth plates in long bones, indicating where bone lengthening occurred.

Articular Cartilage

The smooth, white tissue that covers the ends of bones where they come together to form joints, enabling smooth movement and absorbing shocks.

Epiphyseal Plate

A layer of hyaline cartilage where growth in length of the long bones occurs.

Zone of Proliferation

A region in growing bone where cartilage cells are produced and divide, contributing to bone lengthening.