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

question 24

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.
- $$y ^ { \prime } = y - e ^ { x } - 1 , y ( 1 ) = 2 , d x = 0.5$$

• A) y1 = 1.6409, y2 = 0.2704, y3 = -5.3889
• B) y1 = 2.1409, y2 = 1.5704, y3 = -5.0389
• C) y1 = 0.6409, y2 = -2.3296, y3 = -6.0889
• D) y1 = 1.1409, y2 = -1.0296, y3 = -5.7389

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Definitions:

Pyroclastic Material

Fragmented material ejected during volcanic eruptions, including ash, bomb, lapilli, and volcanic blocks, which varies in size, shape, and composition.

Mudflows

Rapid downhill movement of water-laden earth materials, primarily composed of fine-grained soils and clays, which can cause significant erosion and damage.

Pyroclastic Flow

A hot, fast-moving and deadly mixture of gases, ash, and volcanic material produced by explosive eruptions.

Scoria

A highly vesicular, dark colored volcanic rock that may or may not contain crystals, typically formed from the cooling of lava.