H. Use the gradient to find the equation of the tangent plane to each of the surfaces at the given point. a) x² + 3x²y-z = 0 at (1,1,4) (Answ: 9x+3y-z = 8) b) z = f(x, y, z) = r²y³z at (2,1,3) (Answ: 4x - 3y -z = 2) I. In electrostatics the force (F) of attraction between two particles of opposite charge is given by (Coulomb's law) where k is a constant and r = (x, y, z). Show that F is the gradient T (Hint: ||||||(x, y, z)||). Important problem! F(r) = k₁ of P(7) ||7-1³ -k ||1| =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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H. Use the gradient to find the equation of the tangent plane to each of the surfaces at the given point.
a) x² + 3x²y-z = 0 at (1,1,4) (Answ: 9x+3y-z = 8)
b) z = f(x, y, z) = r²y³z at (2,1,3) (Answ: 4x - 3y -z = 2)
I. In electrostatics the force (F) of attraction between two particles of opposite charge is given by
(Coulomb's law) where k is a constant and r = (x, y, z). Show that F is the gradient
T
(Hint: ||||||(x, y, z)||). Important problem!
F(r) = k₁
of P(7)
||7-1³
-k
||1|
=
Transcribed Image Text:H. Use the gradient to find the equation of the tangent plane to each of the surfaces at the given point. a) x² + 3x²y-z = 0 at (1,1,4) (Answ: 9x+3y-z = 8) b) z = f(x, y, z) = r²y³z at (2,1,3) (Answ: 4x - 3y -z = 2) I. In electrostatics the force (F) of attraction between two particles of opposite charge is given by (Coulomb's law) where k is a constant and r = (x, y, z). Show that F is the gradient T (Hint: ||||||(x, y, z)||). Important problem! F(r) = k₁ of P(7) ||7-1³ -k ||1| =
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