Calculus Early Transcendentals

Mathematics

Quiz 13 :

Vector Calculus

Quiz 13 :

Vector Calculus

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Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone img if its density function is img
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Use Stokes' Theorem to evaluate img where img img is the curve of intersection of the plane img and the cylinder img img is oriented counterclockwise as viewed from above.
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A

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Set up, but do not evaluate, a double integral for the area of the surface with parametric equations img
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img

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Use Stoke's theorem to evaluate img img C is the curve of intersection of the plane z = x + 9 and the cylinder img
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The temperature at the point img in a substance with conductivity img is img Find the rate of heat flow inward across the cylindrical img
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Use a computer algebra system to compute the flux of F across S. S is the surface of the cube cut from the first octant by the planes img img
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Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find img , where a is the constant vector.
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Suppose that img where g is a function of one variable such that img .Evaluate img where S is the sphere img
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Evaluate the surface integral img for the given vector field F and the oriented surface S. In other words, find the flux of F across S. img img
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Find an equation of the tangent plane to the parametric surface represented by r at the specified point. img ; img
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Use Gauss's Law to find the charge contained in the solid hemisphere img , if the electric field is img
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Evaluate the surface integral img for the given vector field F and the oriented surface S. In other words, find the flux of F across S. img in the first octant, with orientation toward the origin.
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Use Stokes' Theorem to evaluate img where img and img is the triangle with vertices img img is oriented counterclockwise as viewed from above.
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Use Stokes' Theorem to evaluate img img img is the part of the paraboloid img that lies inside the cylinder img oriented upword.
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Use Stokes' Theorem to evaluate img where img img is the circle img . img is oriented counterclockwise as viewed from above.
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Evaluate the surface integral. Round your answer to four decimal places. img S is surface img
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Evaluate the surface integral. img S is the part of the plane img that lies in the first octant.
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A fluid with density img flows with velocity img Find the rate of flow upward through the paraboloid img
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Match the equation with one of the graphs below. img
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Use the Divergence Theorem to calculate the surface integral img ; that is, calculate the flux of img across img . img S is the surface of the box bounded by the coordinate planes and the planes img .
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