Parts c and d only please 12. The temperature at any point on a metal plate...
5. Set up the iterated integral for evaluating SSS, f(r,0,z)dzrdrde over the given region D. D is the prism whose base is the triangle in the xy-plane bounded by the x-axis and the lines y = x and x = 1 and whose top lies in the plane z = 2 – y. z 2 z = 2 - y y = x
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
1 R 12. Use the transformation T: u = -x and very to evaluate the integral [jx?dA where R is the region bounded on the xy-plane by the ellipse 9x + 4y = 36. . Let S be the image of Runder T on the uv-plane. Sketch regions and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S Y
The temperature of points on an elliptical plate x² + y2 + xy s 4 is given by the equation T(x,y)=9(x² + y2). Find the hottest and coldest temperatures on the edge of the elliptical plate. Set up the equations that will be used by the method of Lagrange multipliers in two variables to solve this problem. The constraint equation is The vector equation is =1(O The hottest temperature is degrees. The coldest temperature is degrees.
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...
1 3 12. Use the transformation T: u = -x and very to evaluate the integral [JxºdA where R is the region R bounded on the xy-plane by the ellipse 9x² + 4y2 = 36. Let S be the image of R under T on the uv-plane. Sketch regions R and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S...
Please show and explain your steps and please show the graph the before and after the transformation like in the picture, thank you. 12. Use the transformation T: u = -x and v=ķy to evaluate the integral ſf xdA where R is the region R bounded on the xy-plane by the ellipse 9x² + 4y2 = 36. . Let S be the image of R under T on the uv-plane. Sketch regions R and S. Set up the integral 7as...
1 R 12. Use the transformation T: u = 5x and v= ky to evaluate the integral ſf xºdA where R is the region bounded on the xy-plane by the ellipse 9x’ +4y? = 36. . Let S be the image of Runder T on the uv-plane. Sketch regions R and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S...
The temperature at point (x,y) on a metal plate is T(x.y) 16x -16xy+4y.An ant on the plate walks around the The minimum temperature isdegrees. The maximum temperature isdegrees. are the highest and
11. The figure shows the contour map of the function T (in "C giving the temperature at each point (r, y) on an 8cm x 5 cm rectangular metal plate. Use it to estimate the rate of change of the temperature at the point (3,2)in the positive r-direction and in the positive y-direction. 4 75 80 105 00 9508:s 0 11. The figure shows the contour map of the function T (in "C giving the temperature at each point (r,...