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Consider the differential equation \(\dfrac{dy}{dx} = x^2\) with the initial condition \(y(0)=1\).
  1. Use Euler's method with a step size of \(h=0.5\) to find an approximate value for \(y(1.0)\).
  2. By solving the differential equation, find the particular solution for \(y(x)\).
  3. Calculate the percentage error in your approximation from part (a), correct to 3 significant figures.
  4. By considering the concavity of the solution curve, explain whether your approximation in part (a) is an overestimate or an underestimate.

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