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A: Simpsons rule
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A: NOTE: Refresh your page if you can't see any equations. . take integration ...............(1)
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A: NOTE: Refresh your page if you can't see any equations. . take derivative
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A: We will find the required value by simpson 1/3 rule for n=4.
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- The curve ax4+bx3+cx2+dx+k passes thru P1 (5, –210), has a critical point at P2 (4, –416), and an inflection point at P3 (2, 0) where a,b,c,d,k are non zero constants. 1. What are the values of a,b,c,d,k? 2. What type of critical point is P2?We want to estimate f(1.01 , 0.97) for the function f(x,y)= √(4 - x2 - y2). For this, we can use an appropriate linearization of the function f(x,y).Then Fx (1,1) = ? and Fy (1,1) = ? therefore we can estimate the mentioned value obtaining an answer of f( 1.01 , 0.97) ≈ L( 1.01, 0.97) =Suppose ƒ is differentiable on (- ∞, ∞) andƒ(5.01) - ƒ(5) = 0.25. Use linear approximation to estimate the value of ƒ'(5).
- Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all terms in exact form (do not use decimal approximations).Expand x^2y+3y-4 about the point (-1,2) by Taylor's theoremSuppose 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?
- If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval I = ]-∞,0[ Determine if the functions y1 and y2 are Linearly independent or Linearly dependentSuppose that y' = f(y) has no constant solutions, where f : R -> R is infinitely many times differentiable at all points in R. What is the behavior of solutions to y' = f(y).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. 1.dxdt=−x3+xy2,dydt=−2x2y−y3; asymptotically stable