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We will create a parallelogram that approximates it

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Unformatted text preview: s it. Once the parallelogram is created we can easily find the area of it using what we learned from chapter 10. Area of Parallelogram = We know the tangent plane approximates the surface well near . Two vectors that lie in the tangent plane are and . For our small parallelogram, our movement in the x and y direction is not one, but a small change of and . So our vectors that represent the sides of the parallelogram are: and Thus the Area of Parallelogram can be derived below: Thus And finally the Surface Area = Example: Find the surface area of the portion of the paraboloid lying above the xy-plane. We need to know the projection of the surface in the xy-plane: Let z = 0 to get the projection: We need our partials to plug into the formula: ( Notice the change of coordinates to polar to make the limits a lot easier to find ) Summary of Section 13.4 1 Setting up and Evaluating a double integral that represents the Surface Area of a given surface Section 13.5 Triple Integrals For now we will start with an integrand...
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