Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

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Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

Q: The function f defined by the rule f(z, y) = In(xy) increases fastest in the direction of T. F (1,…

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Q: Find the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01,…

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Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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Q: Find the linear approximation of the function f (x, y, z) (3, 2, 6) and use it to approximate the…

A: Given that  f(x,y,z)=√(x^2+y^2+z^2) To find the linear approximation of f(x,y,z) and also find the…

Q: Let f(x,y) = x² – 8x + 2y² + 4y + 7. a. Find and classify all critical points of f.

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Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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

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Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: Evaluate f fs 2² dS, where S is the portion of x2 + y² + z² = 2 in octant 1.

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x2 + y2 + 1 at a. (0, 0), b.…

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

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Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

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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: Find the linearization of the function f (z) =23 at z = 1. L(z) = Using this linearlization, f…

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Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

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Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: Let f (x, y) = x³ + y? – 4xy + 3x + 2y + 5. Find and classify all critical points of f.

A: *concept:- maxima and minima in partial derivatives.

Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

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

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

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Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: Let f(x, y) = xy+ + 2x²y + 4y5 (a) Find fr- (b) Find fy-

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Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

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

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Q: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).

A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

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

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Q: Let f(x, y) = 4x² + 5xy + 2y? – 2x – 3y +1. Find all critical points, and state what type they are.

A: Given: f(x, y)=4x2+5xy+2y2-2x-3y+1 We have to find all the critical points and state their type.…

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

Q: Consider the function f(z) = 728 + 10z5 – 2r2 – 6. An antiderivative of f(x) is F(x) = Ar" + Bx™ +…

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Q: f (x, y, z) = x² + y² + z² and u = (1,0, 1) at P(1, 1, 1).

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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…

Q: Show that the function f(x, y) = x²y% + y° is homogeneous.

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Q: ) Find the direction in which f (x, y) = x²+xyincreases most rapidly at P(1, –1).

A: 1.) given multivariable function is, fx,y=x2+xy and point is P(1,-1). Divergence: Divergence of the…

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = 3x - 4y + 5 at a. (0, 0), b.…

A: fx, y=3x-4y+5 Partially differentiating with respect to x, we get fxx, y=31-0+0=3 Partially…

Q: find the potential function for F= (6x+5y)i+(5x+4y)j Select one: а. f(x,y) = 3x² +5xy + 3y? %3D b.…

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Q: X+Z+3Siny X +2y-2

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Q: show that the L operator is linear for y" – 4y" + 2y' + y = x2

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Q: Compute SA f dA for A = {(x, y) E R² ; x > 0, y > 0 and æ + y < 1} and f: A → R, ƒ(x,y) = xy.

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Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.