Question

7 significant digits please

+ 2y2-10, the spherex-+ y2 + z2-5, and the plane x + 2y+ 3z- (1 point We can use Newton's method to estimate an intersection pont of the c inder 3x Collecting the equations and putting them in standard form, we can write (v)-v -50,wherey Suppose we start with the initial guess o0 The Jacobian there is The function value is And v,-Vo -Jo fvo) is equal to

Answer 1

The 1st function is f1(v1,v2,v3)- 3*v12+ 2*v242 - 10 The 2nd function is f2(v1,v2,v3)- v1A2 v2A2 v3A2-5 The 3rd function is f3(v1,v2,v3)- v1 2*v23 v3-1 The Jacobian Matrix is [ 6*v1, 4*v2, 0 1 [ 2*v1, 2*v2, 2*v3] For initial condition v1-1.000000 v2-0.000000 v3-1.000000 Function value for initial condition is f1(1,0,1)--7.000000 f2(1,0,1)--3.000000 f3(1,0,1)-3.000000 Jacobian matrix for initial condition is [6, 0, 0) [2, 0, 2] Inverse of Jacobian matrix for initial condition is [ 1/6, 0, 0 1 for v1-v0 (J(vo))A-1)f(vo) 2.16666666666667 2.58333333333333 1.33333333333333