1. 2. (1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization...
Find the linearization L(x.y) of the function f(x,y)=x2 - 4xy+1 at P.(3,3). Then find an upper bound for the magnitude |El of the error in the approximation f(x,y)=L(x,y) over the rectangle R: 1x - 3|50.3, y-3|50.3. The linearization offis L(x,y)= The upper bound for the error of approximation is E(x,y) (Round to the nearest hundredth as needed.)
Find the linearization L(x,y) of the function f(x,y)=X - 9xy +7 at Po(5.2). Then find an upper bound for the magnitude El of the error in the approximation fix.y) LIX.y) over the rectangle R X-5 30.5, ly-2 30.5. The linearization of fis Lix,y)=
(1 point) Find the linearization of the function f(x,y) = 72 - 4x² – 2y at the point (3, 4). L(x,y) Use the linear approximation to estimate the value of f(2.9, 4.1) f(2.9, 4.1)
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Please complete #3. 2. Let f(x,y,z 3x2 + 4y2 +5z2- xy - xz - 2zy +2x -3y +5z. Apply 20 steps of Euler's method with a step size of h 0.1 to the system x'(t) y(t)Vf(x(t), y(t), z(t)) z'(t) (x(0), y(0), z(0)) = (-0.505-08) to approximate a point where the minimum of f occurs. Give the value of x (2) (which is the x coordinate of the approximate point where the minimum occurs). Note: This process is called the modified...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
Question 9 Let f(x,y) = y Væety. Find the linearization of f at (1, -1). Use the linearization to approximate f(0.9, -1.1).
5. Let F(x, y, z) = (yz, xz, xy) and define 2 Crin = {(x,y,z) : x2 + y2 = r2, 2 = h} Show that for any r > 0 and h ER, le F. dx = 0 Crih
(1 point) Let F = xi+ (x + y) 3+ (x – y+z) k. Let the line l be x = 4t – 3, y = — (5 + 4t), z = 2 + 4t. = (20, Yo, zo) where F is parallel to l. (a) Find a point P P= Find a point Q = (x1, Yı, z1) at which F and I are perpendicular. Q - Give an equation for the set of all points at which F...