Walking on a surface Consider the following surfaces specified in the form z = ƒ(x, y) and the oriented curve C in the xy-plane. a.In each case, find z’(t). b.Imagine that you are walking on the surface directly above the curve C in the direction of positive orientation. Find the values of t for which you are walking uphill (that is, z is increasing). z = 4x2 - y2 + 1, C: x = cos t, y = sin t; 0 ≤ t ≤ 2π

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.