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Chapter 14: Q. 7 (page 1119)

Give a smooth parametrization of the upper half of the unit sphere in terms of x and y.

Short Answer

Expert verified

a

Step by step solution

01

Step 1. Given Information.

A unit sphere in terms of x and y is given.

02

Step 2. Smooth parameterization.

a

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Most popular questions from this chapter

Do the vectors in the range of F(x,y)=xi+yjpoint towards or away from the origin?

Compute dS for your parametrization in Exercise 7.

ComputethecurlofthevectorfieldsinExercises23–28.F(x,y,z)=sin-1(xy)i+ln(y+z)j+12x+3y+5z+1k

Integrate the given function over the accompanying surface in Exercises 27–34.
f(x,y,z)=yx4z2+1, where S is the portion of the paraboloid z=x2+y2that lies above the rectangle determined by 1≤x≤eand 0≤y≤2in the xyplane.

fx,y,z=1xlnz+2y, where Sis the surface given by ru,v=2ui+u+vj+2u-2vkfor 3≤u≤7and2≤v≤10.
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