Let W(s, t) = F(u(s,t), v(s, t)) where F, u and v are differentiable and u(2,0) = 4 v(2, 0) = 1 Us(2,0) = -2 vs(2, 0) = 3 u;(2,0) = 6 v;(2,0) = 4 Fu(4, 1) = -1 F,(4, 1) = 10 Then W;(2, 0) = and W,(2, 0)=

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Q: 5. Compute F-dà where F= zk and Sis the rectangular plate with corners (0, 0, 0), (1, 0, 0), (0, 1,…

A: To find -   Concept used -

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A: We want to find the gradient of the given function at point (-2,2,-1).

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Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

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Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

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Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

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Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: Find a linearization L(x, y, z) of f(x, y, z) = x²y + 4z at (1,-1,2).

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Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

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A: We have to find

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A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: Find a function f (x, y, z) such that ∇f =〈z, 2y,x〉.

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A: Given:

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A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

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Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

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Q: A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1,…

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Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y – 3z²) ; (7,7,7) O…

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Q: Assume that z = ƒ(x, y), x = g(t), y = h(t), ƒx(2, -1) = 3, and ƒy(2, -1) = -2. If g(0) = 2, h(0) =…

A: We use the partial derivatives to find dz/dt  Then plug x=g(t) and y=h(t)

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Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x,…

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Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(4) = – 4, g'(4) = 9,…

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Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

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

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Q: Find the linearization of the function at the given point. f(x,y,z) = 10xy + 7yz+ 9zx at (1,1,1) O…

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Q: Let f(x, y) = xcosy- y'e*y. fxy at (1,0)is equal to: %3D -2/3 -2 1 0.

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (7xy + 13xz + 17yz)²]. O…

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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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:…

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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…

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A: Given that :-    f(x,y,z)=ln(x+y+z) find out :-   fz(1,0,0)=?

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: prove that x^2y/(x^2+y^2) is not differentiable at 0,0 when  x^2y/(x^2+y^2) if (x,y) not equal to…

A: f(h,k)-f(0,0) =hfx(0,0) +kfy(0,0) +h2+k2∅(h,k) h2kh2+k2-0 =hA+kB+h2+k2ϕh,k ...(1) A =fx(0,0)…

Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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Q: Evaluate f(x, y, z) ds. Js f(x, y, z) = x2 + y2 + z2 S: x + y = 36, 0 SxS 6, OszS X %3D !3!

A: To evaluate:

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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

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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.