Concept explainers
Finding Surface AreaIn Exercises 3–16, find the area of the surface given by
R: square with vertices
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Calculus
- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?arrow_forwardThe y-axis along with the graphs of y=-2x+7 and y=x+2 encloses a triangular region. Find the area of that region.arrow_forwardTutorial Exercise Find the area of the part of the plane 3x + 2y + z = 6 that lies in the first octant. Part 1 of 5 2 The surface S is the graph of a function z = f(x, y) over a region D in the xy-plane. The surface area of S can be calculated by A(S) = az 1 + dz dA. ду f(x, y) = 6 – 3x az 2y. We, therefore, have ax əz -3 and -2 The plane 3x + 2y + z = 6 is the graph of the function z = 3.x ду Part 2 of 5 Therefore, =7 V1+(-3)² + (-2)² dA = V14 dA. Since we want the area of the section of the plane that lies above the first octant, then the region D will be the triangular region bounded by the x-axis, the y-axis, and the line formed by the intersection of the plane with the plane z = 0. Substituting z = 0 into 3x + 2y + z = 6 and solving for y, we find that this line of intersection has the equation y = x + Submit Skip (you cannot come back)arrow_forward
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