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Bell number problem
A set partition of [n] = [1,..., n] is a Bell number B(n) if and only if it contains all the elements of the set.
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- 2. Give the condition which ensure that |ez| < 1 where z in C.Let an bigger or equal 0 and sn = a1 + a2 + . . . + an (and s0 = 0). Prove that if an is divergent, then an/1+sn-1 is divergent. Tip(wskazówka): ComparePlz give correct solution. Suppose T in L(F^2) and dim E(3, T) = 2. Prove that T is invertible.
- Use the chain rule to find ∂w/∂t given w =√ x^2 + y^2 + z^2 and x = cos(st), y = −2s ln(t) and z = s − 3t.(a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by expressing u directly in terms of x, y, and z before differentiating. Then (b) evaluate ux, u y, and uz at the given point (x, y, z). u = e^(qr) sin-1 p, p = sin x, q = z^2 ln y, r = 1/z; (x, y, z) = (pai/4, 1/2, -1/2)1. Find the natural cubic spline sN (x) passing through the 3 points (xj, yj) given by (0, 2), (2, 3), and (3, 1).Then evaluate sN (1).
- ELEMENTARY APPLICATION OF DE/LINEAR DE OF ORDER, n, Case 1 and 2XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1). Which of the following can be used to prove that △XYZ is isoscelesa). Deternine if the DE is classified as Variable Seperable DE or Homogeneous DE. If the DE is Homogeneous, what is the degree of homogenity? b). Find the general solution of the DE shown.
- Consider w=w(x,y,z) Find (∂w / ∂x )and (∂w / ∂y ) and (∂w / ∂z )by implicit derivation and confirm that the result obtainedLooking Ahead Use the Wronskian to show that {e' , te' I is linearly independent on R.Find the value v,w,x,y,z using G.E.M(gauss elimination method) or G.J.M(gauss Jordan method)
