MATH 218 Final Exam Questions And Answers Latest Update 2025

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MATH 218 Final Exam Questions And Answers Latest Update 2025

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2024/2025

MATH 218 Final Exam Questions
And Answers Latest Update
✔✔
Linearization formula ANS L = integral from a to b of f(g(t), h(t), k(t)) |v(t)| dt

gradient field ANS ✔✔ delta g = (dg/dx)i + (dg/dy)j + (dg/dz)k
work equation ANS ✔✔ W = integral from a to b of (Mdx + Ndy + Pdz) dt
Flux equation ANS ✔✔ Flux = integral of M1dy - N1dx + integral of M2dy - N2dx
(both w.r.t. t)

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

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

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

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

surface area of implicit ANS ✔✔ |S| = double integral of | gradient F | / | gradient
f dot p |
AKA length over abs value

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

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