Use Euler's Method to Make a Table of Values for the Approximate

question 63

Multiple Choice

Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.15. $y^{t}=4 x+2 y, \quad y(0) =2$

• A)
• \(\begin{array}{|l|l|l|l|l|l|l|}
• \hline n & 0.000 & 1.000 & 2.000 & 3.000 & 4.000 & 5.000 \\
• \hline x_{n} & 0.000 & 0.650 & 0.800 & 0.950 & 1.100 & 1.250 \\
• \hline y_{n} & 2.000 & 3.100 & 3.970 & 5.191 & 6.868 & 9.139 \\
• \hline
• \end{array}\)
• B)
• \(\begin{array}{|c|c|c|c|c|c|c|}
• \hline n & 0.000 & 1.000 & 2.000 & 3.000 & 4.000 & 5.000 \\
• \hline x_{n} & 0.000 & -0.100 & 0.050 & 0.200 & 0.350 & 0.500 \\
• \hline y_{n} & 2.000 & 2.350 & 3.220 & 4.441 & 6.118 & 8.389 \\
• \hline
• \end{array}\)
• C)
• \(\begin{array}{|c|c|c|c|c|c|c|}
• \hline n & 0.000 & 1.000 & 2.000 & 3.000 & 4.000 & 5.000 \\
• \hline x_{n} & 0.000 & -0.350 & -0.200 & -0.050 & 0.100 & 0.250 \\
• \hline y_{n} & 2.000 & 2.100 & 2.970 & 4.191 & 5.868 & 8.139 \\
• \hline
• \end{array}\)
• D)
• \(\begin{array}{|l|l|l|l|l|l|l|}
• \hline n & 0.000 & 1.000 & 2.000 & 3.000 & 4.000 & 5.000 \\
• \hline x_{n} & 0.000 & 0.150 & 0.300 & 0.450 & 0.600 & 0.750 \\
• \hline y_{n} & 2.000 & 2.600 & 3.470 & 4.691 & 6.368 & 8.639 \\
• \hline
• \end{array}\)
• E)
• \(\begin{array}{|c|c|c|c|c|c|c|}
• \hline n & 0.000 & 1.000 & 2.000 & 3.000 & 4.000 & 5.000 \\
• \hline x_{n} & 0.000 & 0.500 & 0.650 & 0.800 & 0.950 & 1.100 \\
• \hline y_{n} & 2.000 & 2.950 & 3.820 & 5.041 & 6.718 & 8.989 \\
• \hline
• \end{array}\)

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Definitions:

Confidence Interval

A range of values, derived from the sample data, within which the population parameter is expected to lie, with a specified level of confidence.

Blood Donors

Individuals who voluntarily have their blood drawn for the purposes of transfusion, research, or donation.

Large-Sample Z

A statistical test used to infer the population mean from a sample mean when the sample size is large, typically using the Z-distribution.

Significance Levels

A threshold chosen by the researcher which determines the probability of rejecting a true null hypothesis, often denoted by alpha (α).