(d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

A:

Q: Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7) where g(x, y) =…

A: According to our policy at Bartleby, I can solve only 1 question. Given a function : g(x,y)=12x+5y2…

Q: 3. find the derivative of the function at Po in the direction of u. f (x, y,z) = 3e* cos yz,…

A:

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

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 partial derivative of f (x, y) = e2+3y cos (x³y²) with respect to x. O fa (x, y) = e2x+3y…

A: Given f(x,y)=e2x+3ycosx3y2 To differentiate f(x,y) partially with respect to x Let u=e2x+3y…

Q: Find the linearization of the function f(x,y) = V9x² + 16y² at the point (1, 1), and use it to…

A:

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

A:

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: Q2. Find the second order partial derivative of F(x.y) = x³+ x°y°- 2y² w.r.t. x at (2,1).

A: Given:        Fx,y=x3+x2y3-2y2  taking first partial derivative with respect to x.…

Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

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

A:

Q: For f(x,y,z)=3xy+2y+8z - cos(x²+y²–z), the partial derivative fxy(1,2,5)=

A: Given function is fx,y,z=3xy+2y+8z−cosx2+y2−z. We have to find the partial derivative fxy1,2,5.…

Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

A:

Q: Find the linearization of the function f (x) = x° 26 at æ = 1. a vā |a| sin (a) L (x) = Using this…

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

Q: Find the (absolute) maximum and minimum values of f(x, y) = sin x cos y on the square R = {(x, y)|0…

A: Given,            f(x, y)= sinxcosy                    (1) on the sqaure             R=x, y| 0≤x≤2π,…

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

A:

Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

A:

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

A:

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

A:

Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

A:

Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

A:

Q: (a) f(x) = e" centered at r = 0.

A:

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 fz and fy- Te dt f(x, y) = 5 f.(x, y) f,(x, y) : %3D

A:

Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A:

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

A:

Q: 8. The second directional derivative of a function f(r, y) is D²f(x, y) = D„[D„f(x,y)]. If f(r, y) =…

A: Consider the given function, fx=x3+5x2y+y3 the formula for the second directional derivative of a…

Q: 9. What is the total derivative of f(x, y)=tan(x+ y) at x=",y=0 ? a) df =-2dx-2dy b) df =2dx+2dy c)…

A: This question is related to differentiation, We will solve it using given information.

Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

A:

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

A:

Q: Find the partial derivative for the function f(x,y)=√x+y3 f(xx,y)= f(x,y) = √8x + y² 33x √8x+y³ (y)=…

A: The given function is;  f(x,y)=sqrt(8x+y3).

Q: xY 2. (a) Prove that the function f(x, y) is differentiable everywhere in its do- %3D x2 + y? main.

A: Solution is given below:

Q: (a) Find the first partial derivative of (i) } f(x, y, z) = (ii) f(x,y, z) = eY² cos xy

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

Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: Find fz and fy- f(1, v) = | 3e dt f (x, y) =| f,(a, v) = [

A:

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

A:

Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

A:

Q: (b) Find the partial derivative at point (u,v) = (-4,0) of w = In(xª + yß + zª),x = ue"sinu, y =…

A: Chain rule:  Suppose that  are differentiable functions of and  is a differentiable function of .…

Q: ². I = fő fő fő (x + y + z) dx dy dz

A:

Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

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

Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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