If ∂f/∂y is continuous in the rectangle D, show that there is a positive constant K such that (31) |f(t,y1)−f(t,y2)|≤K|y1−y2| where (t, y1) and (t, y2) are any two points in D having the same t coordinate. This inequality is known as a Lipschitz22 condition. Hint: Hold t fixed and use the mean value theorem on f as a function of y only. Choose K to be the maximum value of |∂f/∂y| in D.

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