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3.- Determine all the second partial derivatives.
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- Why Wronskian determinant W(a) = |X(a)| is nonzero?The trace determinant plane in our textbook (and in We-bAssign) includes two border cases: (1) when τ = 0 (and ∆ > 0), wehave a center point and (2) when τ 2 = 4∆, we have a degenerate node.It does not include the other border case when ∆ = 0.(c) Suppose τ > 0. Is the (0, 0) equilibrium stable or unstable in thiscase? What if τ < 05. Given that, for some a, b, c, d, e, f, g, h, i E R, a b c d e f g h i = 8 evaluate the following deterimants: x = 3g 3h 3i d e f -2a -2b -2c y = d-5g e-5h f-5i a b c g+7a h+7b i+7c z = d -a 2g e -b 2h f -c 2i
- suppose u=f(x,y) and v=g(x,y) with xy+2xu+3xv+Vu-1=0; 2xy+3yu-2xv+2uv+2=0 find the jacobianThe following question is about the volume of an object bounded by parabola x = y^2 - 5y, and straight line y = x. (x, y) in meters. Height of object (in meters), h(x, y) = (y - x)(x - y^2 + 5y) a) Find max height by: i) finding critical points of h(x, y) ii) identify single critical point within cross-sectional area, A (not on boundary) iii) show point found in (ii) is a local max with hessian determinant test iv) evaluate value of h at this max I understand that im only supposed to ask one question at a time but it is hard to follow up on these types of questions over multiple responses. It would really be appreciated if you could help me, or you could possibly credit extra questions from my account. thanks :)Compute the Wransky determinant (Wranskian) of the functions y1, y2, y3 defined below with constants a, b, c y1(x) = 8a + 7x, y2(x) = xln(bx), y3(x) = cx^2
- Explain particular solution of the forced system x'' = Ax + F0 cos wtWhat does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?Find the Jacobian determinant to the test the existence of functional dependence between these three functions- Y1 = 11X1 + 7X2 + 5X3 Y2 = 6X1 + 9X2 + 10X3 Y3 = 11X1 + 11X2 + 15X3 What is the value of the Jacobian determinant ?
- Use Jacobian determinants to test the existence of functional dependence between the paired functions y1 =3x12 + 2x22 y2 = 5x1 +1Find all stationary points of the function f(x,y)= 3x2 -6xy+2y3, and use Hessian Matrix and the determinant to classify each as a local maximum, a local minimum, or a saddle point.The linear operator T: R2 --> R2 defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?
