

The temperature in a rectangular plate is described by the function below: f(x, y) = x^3...
0.5 05 3-) (a) Find the approximate value of the cos' x dr integral using Simpson 1/3 and 3/8 rules. Calculate the absolute error you made by comparing it with its real value. (b) Calculate the fre dx integral Trapezoidal, the absolute error between the Simpson's rule and its true value.
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A. dx 8 X xf (x) 7f(x) dy O B. dx 8 X dy xf(x) 7f(x) O C. dx 8 X 7f'(x) xf(x) dy O D. dx 8 X
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A....
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that dr--Fr 9. Fid the critical points of f(z, y) if any exist, for (a, y) = ex sin y 10. Calculate the iterated integral: ysin(zy)d dy
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that dr--Fr 9. Fid the critical points...
Write an iterated integral for SSS fex,y,z) av. S = {(x, y, z): 0 sxs8,0 sy s5,0<zs (5 - 6x - 2y)} 5 S 5-6x - 2y f(x, y, z) dz dy dx 5 8 5 f(x, y, z) dz dy dx s 8 5 5 - 6x - 2y f(x, y, z) dz dy dx 5 666 8 5 5 - 6x - 2y f(x, y, z) dx dy dz
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
For the following Integration: F(x) = x3 – x dx where: n = 8 (# of pieces) a- Calculate the exact solution for the given integration by using Traditional methods. b- Estimate the integration numerically by using Trapezoid rule and calculate the error. C- Estimate the integration numerically by using Simpson rule and calculate the error.
Reverse the order of integration in the following integral. 6 24 - 4x s s f(x,y) dy dx y = 24 - 4x 0 0 X Reverse the order of integration. f(x,y) dx
as a function of x. Nrite the function below in the form y = f(u) and u = g(x). Then find dy dx y = √5x² - 6x +5 Write the function in the form y=f(u) and u = g(x). Choose the correct answer below. OA. y = Vu and u = 5x2 - 6x + 5 OB. y=u and u =5x2 - 5x+5 OC. y = 5u? - 5u +5 and u = x OD. y = 5u2 -...
Find the temperature distribution at equilibrium in a rectangular plate (0 ≤ x ≤ L, 0 ≤ y ≤ H) when the side at x = 0 is subject to the prescribed temperature f(y) = 1 + y, and the sides at x = L, y = 0 and y = H are insulated, by using the method of separation of variables.
To translate the steepest ascent into matlab code: f(x,y)=-8*x + 12*y + x^2 - 2*x^4 - 2*x*y + 4*y^2 dx=-8+2x-8x^3-2y dy=12-2x+8y subs in x0=0, y0=0 into dx and dy dx=-8 dy=12 subs dx and dy into x1=x0 + dx*0.001 and y1=y0 + dy*0.001 then subs x1 and y1 back to x0 and x0; repeat the step until the answer has reach optimisation.