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Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10
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A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x
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- Find two positive numbers x and y with xy=81 such that x+4y is minimized.Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the square of thedistance.Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975 to its left.
- The paraboloid z = x2 + y2 - 4x + 2y + 5 has a local minimum at (2, -1). Verify the conclusion of as shown for this function.Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter
- In Exercises 36–38, find the point on the given curve closest tothe specified point. Recall that if you minimize the square ofthe distance, you have minimized the distance as well. 36. (1, 1) and √x +√y = 237. (0, 0) and xn + yn = 1 for n a positive, odd integer38. (0, 0) and xn + yn = 1 where n > 2 is a positive, evenintegera. Use the 2nd-order Runge-Kutta Method to approximate y(t) with h= 0.25 b. Use the 4th-order Runge-Kutta Method to approximate y(t) with h=0.25 c. Plot both sets {yi} obtained in (1) and (2) d. Determine the eventual population level (as t→∞) reached from initial population.Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value.