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Numerical Analysis
- A natural cubic spline S is defined byS0(x) = 1+B(x −1)−D(x −1)3, if 1 ≤ x < 2 S1(x) = 1+b(x−2) −3/4(x−2)2 + d(x−2)3, if 2 ≤ x ≤ 3If S interpolates the data (1, 1), (2, 1), and (3, 0), find B, D, b, and d.arrow_forwardExpress K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.arrow_forwardGiven an ellipse of the form {x=m cos(t) {y=n sin(t) prove that the x-intercepts are (-m,0) and (m,0) and the y-intercepts are (-n,0) and (n,0)arrow_forward
- Another way to prove the uniqueness of the midpoint is to assume that there are two midpoints M and N, then conclude that M=N. Prove the midpoint theorem using this method.arrow_forwardFind the complete solution for the DEsarrow_forwardFind the diffrential equation of for each of the curves determined by the condition that ateach point (x, y) where the length of the subtangent is equal to the sum of its coordinates.arrow_forward
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