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satisfies and its graph contains the point .

  1. Use Euler’s Method to sketch an approximation of over . Use .

    Show all steps and carefully record the coordinate points at , , , and .

    Continuous piecewise, left segment starts at (negative 1, comma 5), changing to upward curve at about (0, comma 3.5), turning at about (0.25, comma 3.25), ending at the point (1, comma 4).

  2. Use implicit integration to solve the differential equation.

    Use to help you find the value of after you integrate.

  3. Compare your answers to parts (a) and (b). Determine the largest difference between the actual -value and the Euler’s Method -value for , , , , and . This largest difference estimates the error of Euler’s Method. If instead, do you think this error will be larger or smaller?