Exercises for Question Type 1: Approximating values for a given step length using Euler's method

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Exercises for Question Type 1: Approximating values for a given step length using Euler's method - IB

Question 1

Approximate y (0.1) using Euler’s method with h = 0.05 for \frac{d y}{d x} = x^{2} + y^{2}, given y (0) = 1 .

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Question 2

Use Euler’s method with step size h = 0.1 to approximate y (0.3) for \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 3

Subject: Mathematics, Topic: Differential Equations, Euler's Method.

Use Euler’s method with step size h = 0.2 to approximate y (1.0) for the differential equation \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 4

Euler's Method Approximation

Use Euler’s method with step size h = 0.1 to approximate the value of y at x = 0.4 for the differential equation \frac{d y}{d x} = x^{2} + y^{2} with initial condition y (0) = 1 .

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Question 5

Use Euler’s method with step length h = 0.05 to approximate y (0.2) for the differential equation \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 6

Use Euler’s method with step size h = 0.25 to estimate y (0.75) for the differential equation \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 7

Apply Euler’s method to a first-order differential equation to find an approximate value of y at a given value of x .

Apply Euler’s method with step length h = 0.2 to approximate y (0.6) for the differential equation \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 8

Differential Equations - Euler's Method

Approximate y (2.0) using Euler’s method with a step size of h = 0.5 for the differential equation \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 9

Use Euler’s method with step size h = 0.25 to estimate y (1.0) for \frac{d y}{d x} = x^{2} + y^{2}, given y (0) = 1 .

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Question 10

This question assesses the application of Euler's method to numerically solve a first-order differential equation.

Use Euler’s method with h = 1.0 to estimate y (4) for \frac{d y}{d x} = x^{2} + y^{2}, given the initial condition y (0) = 1 .

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Question 11

Apply Euler's method to approximate solutions of first-order differential equations.

Apply Euler’s method with step size h = 0.1 to estimate y (0.5) for the differential equation \frac{d y}{d x} = x^{2} + y^{2} with the initial condition y (0) = 1 .

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IB Mathematics Applications & Interpretation Question Type 1: Approximating Values for a Given Step Length Using Euler's Method Exercises