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- 5. The derivative is the gradient of the tangent to the function. In the case of a semi-circle, this means that the gradient vector (1, dy/d.r) should be orthogonal to the vector(arn, Y0). Verify this using the dot product and also by plotting both vectors (normalise the gradient vector).Q1: Consider a surface of revolution generated by a Bezier curve defined by the four control points P(0,0,0), (2,1,2), P₂ (3,3,0) P, (2,2,3) respectively, rotating about the X-axis. Calculate the point on the surface at u = 0.25, 0= π/2.Verify that each function is an "eigenfunction" for the given linear operator, and determine it's eigenvalue. (a) First derivative; f(x) = e³x (b) Second derivative; g(x) = sin(2x)
- Find a transformation of a triangle A(1, 0) B(0, 1) C(1, 1) by one unit in x and y translating directions and then rotating 45' about the origin.Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. (a) the characteristic equation - 1 = 0 (b) the eigenvalues (Enter your answers from smallest to largest.) 1 (22, 22) =| 2 2 a basis for each of the corresponding eigenspaces X, = X, = 1Group all 0’s on the Karnaugh map to obtain simplified F’ function
- (Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.Find the derivative of the function. F(x) = -1/12/2 x2 f'(x) =Please solve very soon Derive hamiltonian equation for self-organizing map to reduce the error during each iteration using the weight udating equation and error equation.
- 1. Determine the equation of the line through the given point (a) parallel and (b) perpendicular to the given line Given: Point: ( -1,-4) Line: 4x-2y=3Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 3 -1 1 2 (a) the characteristic equation P (b) the eigenvalues (Enter your answers from smallest to largest.) 1 1 - 2 a basis for each of the corresponding eigenspaces 1 X, = 1 3 X2 1Find the length of the curve y = f (x), for: