7. Find the linearization L(x,y) of the function f(x.y) = x e^xy at the point (2,0), and use it to approximate the value of f(2.1,–0.2) Select one: a. (2.1,–0.2)~2 b. A(2.1,–0.2)~0.9 c. (2.1,–0.2)~1.6 d. A(2.1,–0.2)~1.3 e. (2.1,–0.2)~2.4

Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A:

Q: 7. Compute the gradient of the following function f(x, y, z)= e-2z sin(2y) cos(2y);

A:

Q: find the linearization L(x, y) of the functionƒ(x, y) at the point P0 . Then find an upper bound for…

A: Given, f(x,y)=xy-3y2+2,   P0(1,1) Linearization of function at (a,b) is L(x,y)…

Q: Consider the function g(x, y) = x² + xy + y² (1 + 1/2t, 2 + V3/2t), use the (a) Given the line l(t)…

A: Given,              g(x, y)=x2+xy+y2

Q: Find the linearizations of the functionsat the given points. ƒ(x, y, z) = √2 cos x sin ( y + z) at…

A:

Q: Find the orthogonal trajectories of the family of curve y = 3x+c,where c is an arbitrary constant.

A:

Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

A:

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: Q2: Discuss the fundamental theorem for gradients usingE = 5x2 î + 20 xy j+ 10 yz3 k and the…

A:

Q: Find the orthogonal trajectories of the family of curves xy = a where a ≠ 0is an arbitrary constant.

A: Consider the equation: xy=Cy=Cxy'=-Cx2 Substitute the value of C in the first derivative:…

Q: 2/6 Consider the upper half of the ellipsoid f(x.y) = 1--n and the point P-- 3 on the level curve…

A:

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = (x + y + 2)2 at a. (0, 0), b.…

A: Given function,  f(x, y) = (x + y + 2) 2 To find linearisation L(x, y) at i) (0, 0)  ii) (1, 2)

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

A:

Q: Find the linearization z = = L(x, y) of the function z = f(x, y) = 3.x2 – y² + 5y at the point (xo,…

A: z=fx, y=3x2-y2+5y and the point is x0, y0=2, 1. Now, f2, 1=322-12+51=12-1+5=16 Now partially…

Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

A:

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

A:

Q: Find the linear approximation of the function f (x, y,z)= x' Vy +z° at the point (2, 3, 4) and use…

A: Given:-               Find the linear approximation function f (x,y,z)= x 3y2+z2 at the point…

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

A:

Q: Find the linearization L(x,y,z) of the function f(x,y.z) at the given points. f(x.y.z) = e* + cos (y…

A:

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: 1. Determine if the gradient of the following velocity function is irrotational: V (x, y, z) = 3x³y²…

A:

Q: Find the linearization L(x,y) of the function f(x,y) = e (X cos (5y) at the points (0,0) and 0,- 2

A:

Q: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

A:

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = e2y-x at a. (0, 0), b. (1, 2)

A: Given:fx,y=e2y-x at   a.0,0    b.1,2Formula:Lx,y=fa,b+fxa,b.x-a+fya,b.x-b

Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

A:

Q: Find the maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

A:

Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

A:

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A: Function: f(x,y,z)=xy+yz+zx, at(0,0,0) We need to find fx,fy,fz. at the point (0,0,0)

Q: Find the gradient of the function f(x, y) = 3x + 5y2 + 1, at the given point      (2, 1)

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: 2. Consider the following function F (r, y, z) = x² + 2xyz + y² In z and the point P = (2,1, 1) and…

A: *The given function is, F(x,y,z)=x2+2xyz+y2×lnz *The point P is P=(2,1,1) *The vector u is u=i+2j-2k…

Q: 9. Demonstrate that the functions Y1 = x2, y2 = sin(x), y3 = xe are linearly independent on R.

A: Recall: If y1,y2 and y3 are the given function and         Wy1,y2,y3x = y1y2y3y1'y2'y3'y1''y2''y3''…

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: To find the linearization Lx,y,z of the function at the given points fx,y,z=x2+y2+z2 at 1,0,0

Q: Find the direction at which the function f(x, y, z) = x In(e – xz) increases fastest at (-2, 0, 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

A:

Q: Find the linearization L(x,y) of the function f(x,y) = e* cos (9y) at the points (0,0) and ...

A:

Q: 2. (a) Let z ry, r =r cost and y=r sin t. Compute by using the chain rule and express your answer in…

A:

Q: Find the linearization of the function at the given point. f (x, y) = e sin y, 0, 7).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

A:

Q: 2. Find the maximum value of the directional derivative, D f, of the function _2 f(x, y, z) = x´ +…

A:

Q: #2. Consider the function f (x, y,z) = xy+3xz² + 5y at the point (1,0, 2) (a) Find the direction in…

A:

Q: Find the gradient of the function In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

A:

Q: Exercise 6 Using the method of variation of parameters, the particular solu- tion y, for the DE y" +…

A:

Q: 1. Find the orthogonal trajectories of the family of curve z + 3y = cy,where cis an arbitrary…

A: We will first find the differential equation of the of the given family of curves

Q: Find the linearization of the function f (x, y, z) = -6xy+ 9yz + 8zx at the point (1, 1, 1)

A:

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = tan-1 (xyz) at…

A: Consider a function: fx, y, z=tan-1xyz……1   Given point, say A, is: A=1, 1, 1   On comparing A with…

Q: Find the linearization of the function f(x, y, z) = xy+ yz + zx at the point (1,1,1).

A: Linearization of the function f(x,y,z) at (a, b, c) is given by…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.