example 1 Let D be the region determined by 0 <0 < 21,0

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Example 1 Let D Be The Region Determined By 0 0 21 0 R 1 And Let The Function 0 D R Defined By X R Cose Y R 1 (100.23 KiB) Viewed 27 times

example 1 Let D be the region determined by 0 <0 < 21,0 <r < 1 and let the function 0: D → R?, defined by x=r cose, y=r sine, z=r, be a parametrization of a cone S (see Figure 7.3.8). Find its surface area. 16. Use formula (4) to compute the surface area of the cone in Example 1. Surface Area of a Graph A surface S given in the form z=g(x, y), where (x, y) e D, admits the parametri- zation x = U, y = 0, z = g(u, v) for (u, v) e D. When g is of class C!, this parametrization is smooth, and the formula for surface area reduces to 2 figure 7.3.8 The surface Z= V x2 + y2 is a cone. It is not regular at its tip. A(S) = 11. (16) + (*) +1). ag ax 2 + ag ay da, (4)