u(0,1)= 0, U(1,1)=0, u(x,0)=2x u(x,0)=2 ALE. A Q.4/Answer ONLY TWO, Except (C) (4) Using Lagrange interpolating polynomial, find f(x) when = 2.35? The numbers (called nodes) that available are ( x = 2, f =4), (x₁ = 2.5, f₁=625), (x₂=3. f =9) ?
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- How can you find the first derivative of the given polynomial function? What mathematical skill is essential in finding the critical number(s)? If you will graph the given function using desmos or any graphing utility, what can you say about the maximum and minimum?construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. 2.dxdt=−x3+2y3,dydt=−2xy2; stable (at least)dxdt=−x3+2y3,dydt=−2xy2; stable at leastSuppose that the quadrature formula has degree of accuracy atleast 2 integral f(x)dx with upper limit 2 and lower limit -2 = a1f(−2) + a2f(0) + a3f(2) Use the definition of degree of accuracy to determine the constantsa1, a2, a3, and then determine the exact degree of accuracy of the quadratureformula. Is there any quadrature formula that has higher degree of accuracyand that also uses three functional evaluations?