This assignment covers (vectors, green's theorem. divergence theorem, line integrals, surface...

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This assignment covers (vectors, green's theorem. divergence theorem, line integrals, surface integrals, Lagrange Multipliers, Directional Derivatives, Double Integrals(polar and spherical coordinates), Triple Integrals(polar and spherical coordinates), Parametrized Surfaces, Tangents and Normals to Curves)

Rajeswari · Accepted Answer

Qno.1
Uxv =
 
q.no.4
Thus in uv plane this is square with u ranging from 0 to 1 and v also ranging from 0 to 1
By change of variables the double integral become
Thus we get 0 as answer.
          Cost = 15/sqrt 133 = 1.3006 which is not possible.
Find partial derivatives both I and second order.
We get f_x = 2xy^2-2x:   f_y = 2x^2y-8y:   f_xx = 2y^2-2:   f_yy = 2x^2-8
And f_xy = 4xy = f_yx
Equate first derivatives to 0
0= 2xy^2-2x and 2x^2y-8y=0
Solving we get x=0, y =1, or -1  and y=0, x = 2 or -2
i.e. solutions are (0,0) (-2,1) (2,-1) (2,1) and (-2,

This assignment covers (vectors, green's theorem. divergence theorem, line integrals, surface integrals, Lagrange Multipliers, Directional Derivatives, Double Integrals(polar and spherical...

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