You know from the text that the graph of the equation x2 + y2 = 9 is a circle with center (0, 0) and radius 3. In Exercise, use a graphing utility to investigate what happens when the equation is changed slightly. (As in graphing circles, you’ll first need to solve the given equations for y.)
(a) x3 + y3 = 9
(b) x5 + y5 = 9
(c) On the same set of axes, graph the equations given in parts (a) and (b). On the basis of the pattern you see, what do you think the graph of the equation x7 + y7 = 9 will look like? Draw a sketch (by hand) to show your prediction. Then use a graphing utility to see how accurate your prediction is.
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