f(x, y, z) = ln(x² + y² + z²) at the point P(1, 3, 2) in the direction of

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: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: Find the gradient of the function f(x, y, z) = yz², at the point (0, -1,–1) V f(0, –1, –1) =

A: fx, y, z=yz2 & the point is 0, -1, -1. Partially differentiating with respect to x, we get fxx,…

Q: Calculate the directional derivative of the function f(x, y, z) = 2x³y − ln(y)x²z − z² at the…

A: Answer

Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

A:

Q: Find the linearization L(X,Y) of the function  f(x,y)=y-1/x+1 at(0,0).

A:

Q: Let f(x, y) = exy and P(1, 0). Solve for the gradient of f at the point P.

A:

Q: Find the direction at which the function f(x, y, z) = x In(e – az) increases fastest at (-3,0, 0) O…

A:

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t² at t=1

A: I have solved the problem with two methods.Final solution is in the box.

Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

A:

Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 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:

Q: Find the gradient of the function f(x,y,z)=y^(2)ln(xz), at the point (1,−1,e) ∇f(1,−1,e)=?

A: Given query is to find the gradient of f(x,y,z) at a point (1,-1,e).

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

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: Find the gradient of f(r, y, z) = xy?z³ + In(ryz) at the point (1, 1, 1).

A:

Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

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

A: Consider the following function: fx,y=excosy Differentiate fx,y with respect to x taking y as…

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: Consider h(x, Y, z) = cos (xy) + eY% + ln (xz). Determine the directional derivative of h at the…

A:

Q: Find the derivative of the function at Po in the direction of vector A h(x, y, z) = cos(xy) + e>% +…

A:

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

A:

Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector…

A: Solution:-

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: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

Q: Find the gradient of the function f(x, Y, z) = y² ln(za), at the point (e, –1, 1) Vf(e, –1,1) =

A: The given function fx,y,z=y2ln(zx)

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

A:

Q: Q1: Find the derivative of f(x,y,z)=x^2+yx^2-3z at point P_o (1,1,0) in the direction of vector V…

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

Q: Find the gradient of f(x,y,z)=xy+yz+xz at point P(1,2,3).

A: As we know that the expression for the gradient is: ∇fx,y,z=i∂∂x+j∂∂y+k∂∂zfx,y,z Given:…

Q: Find the directional derivative of f(z, y) = In(e" - 3y) at the point (0,0) in the direction of 3i +…

A:

Q: dz Use the Chain Rule to find : z = = cos(x + 4y),x = 5t*, y = - %3D dt

A:

Q: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i…

A:

Q: Find the gradient of the function f(x,y, z) = xy°z³ at the point (1,1,1).

A:

Q: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

A:

Q: Find the linear approximation to f(x, y, z) = " at the point (2, –1, 1): f(x, y, z) =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

A:

Q: Find the maximum rate of change in f (x, y, z) = tan(r + 2y + 3z) at P = (-5,1,1).

A:

Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: Determine the linearization of f(x, y) = arctan(x² + y²) at

A:

Q: Find the gradient of f(x,y,z) = sin x ln y + z^3

A:

Q: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here

Q: If f(x,y,z)=xe^(2y)sin(8z), then the gradient is ∇f(x,y,z)=

A:

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…

Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣

A: