MATH 218 Final Exam Prep with Questions and Answers

MATH 218 Final Exam Prep with
Questions and Answers
Linearization formula ANSWER L = integral from a to b of f(g(t), h(t), k(t)) |v(t)| dt



gradient field ANSWER delta g = (dg/dx)i + (dg/dy)j + (dg/dz)k



work equation ANSWER W = integral from a to b of (Mdx + Ndy + Pdz) dt



Flux equation ANSWER Flux = integral of M1dy - N1dx + integral of M2dy - N2dx

(both w.r.t. t)



how to tell if conservative ANSWER conservative if dM/dy = dN/dx, dM/dz = dP/dx, and
dN/dz = dP/dy



greens theorem flux ANSWER flux = double integral over R of (dN/dx + dM/dy) dxdy



greens theorem circulation ANSWER circulation = double integral over R of (dN/dx -
dM/dy) xydy



surface area of explicit ANSWER |S| = double integral of sqrt (1 + (fx)^2 + (fy)^2) dxdy



surface area of implicit ANSWER |S| = double integral of | gradient F | / | gradient f dot p |

AKA length over abs value



surface area of parametric ANSWER |S| = |ru x rv| dudv WHERE ru is derivative w.r.t. u and
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