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Chapter 13: Vector Calculus

Expert-verified
Essential Calculus: Early Transcendentals
Pages: 755 - 830
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

336 Questions for Chapter 13: Vector Calculus

  1. If \({\rm{F = Pi + Qj}}\). how do you test to determine whether F is conservative? What if F is a vector field on \({\mathbb{R}^3}\)?

    Found on Page 830

  2. Find the value of\(\iint_S xzdS\)

    Found on Page 817

  3. : Use a computer to graph the parametric surface. Get a printout and indicate on it which grid curves have u constant and which have v constant

    Found on Page 805

  4. \({\bf{F}}(x,y,z) = z{\bf{i}} + y{\bf{j}} + zx{\bf{k}}\), \(S\) is the surface of the tetrahedron enclosed by the coordinate planes and the plane

    Found on Page 829

  5. Evaluate the line integral, where \({\rm{C}}\) is the given curve

    Found on Page 771

  6. Use Green’s Theorem to evaluate the line integral along the given positively oriented curve.

    Found on Page 788

  7. Sketch the vector field by drawing a diagram like Figure 4 or Figure 8.\(F(x,y,z) = j - i\)

    Found on Page 760

  8. Determine whether of not \({\bf{F}}\) is a conservative vector field. If it is, find a function \(f\) such that\({\bf{F}} - \nabla f\).

    Found on Page 780

  9. Find the work done by the force field

    Found on Page 830

  10. If \({\rm{F}}\) and \({\rm{G}}\) are vector fields, then \({\mathop{\rm curl}\nolimits} ({\bf{F}} \cdot {\bf{G}}) = {\mathop{\rm curl}\nolimits} {\bf{F}} \cdot {\mathop{\rm curl}\nolimits} {\bf{G}}\).

    Found on Page 830

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