Euler's Method and Approximations

The video tutorial explains how to use Euler's method with a step size of 0.4 to estimate the value of y at x=2 for a given initial value problem. The process involves calculating successive x and y coordinates using a recursive formula. The tutorial walks through each step, calculating slopes and y values, ultimately finding that y(2) is approximately 21.48351.

What is the step size used in Euler's method for this problem?

• 0.2

• 0.4

• 0.8

• 0.6

What is the initial condition given for y(x)?

• y(0) = 2

• y(0) = 1

• y(0) = -1

• y(0) = 0

How is the next x coordinate calculated in Euler's method?

• Dividing by the step size

• Subtracting the step size

• Multiplying by the step size

• Adding the step size

What is the x coordinate when x sub 5 is reached?

• 2.0

• 1.6

• 2.8

• 2.4

What is the formula used to calculate y sub 1 in Euler's method?

• y sub 0 + f(x sub 0, y sub 0) * delta x

• y sub 0 - f(x sub 0, y sub 0) * delta x

• y sub 0 * f(x sub 0, y sub 0) / delta x

• y sub 0 / f(x sub 0, y sub 0) + delta x

What is the value of y sub 2 after calculation?

• 1.28

• 2.56

• 1.92

• 0.64

What is the slope at the point (0.8, 0.64)?

• 2.08384

• 0.64

• 3.6096

• 1.6

What is the approximate value of y sub 4?

• 9.14239

• 7.54080

• 5.74080

• 3.6096

What is the final approximate value of y(2) using Euler's method?

• 22.48351

• 21.48351

• 20.48351

• 19.48351

What is the main purpose of using Euler's method in this problem?

• To eliminate the need for initial conditions

• To find the exact solution

• To approximate the solution

• To simplify the equation