Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental form of o. 2. Compute the normal curvature and the geodesic curvature of the circle y(t) = (sint, cost, 1) on the above paraboloid.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.