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EXAM 3 Outline - written as an iterated integral 6 Know how...

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EXAM 3 Outline 1. Know the second derivative test for functions of two variables involving the determinant of the Hessian matrix. 2. Know that a definite integral is a limit of Riemann sums and know that length, area, volume, etc. are limits of approximating sums 3. Know the statement of the Fundamental Theorem of Calculus and why the theorem is fundamental. 4. Know the definitions of double and triple integrals in Cartesian coordinates. 5. Know the theorem that for a simple region E, a multiple integral over E can be
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Unformatted text preview: written as an iterated integral. 6. Know how to calculate areas and volumes with double integrals in both Cartesian and polar coordinates. 7. Know how to calculate volumes with triple integrals in Cartesian, cylindrical, and spherical coordinates. 8. Know how to calculate centroids and centers of mass in Cartesian, cylindrical and spherical coordinates. 9. Pappus’s 1 st Theorem....
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