Let f(x, y, z) 75 Then Vf = and Duf(1,3, -3) in the direction of (-1, -2, -2) is

Q: Let f(x,y) =x2-xy+y2-x. Find the direction u and the value of Duf(1, -1) for which D,f(1,-1) is…

A: Directional derivative problem....

Q: Determine D„f(4, –1,6) for f(x,y,z) = ex³y + 4zx³ in the direction of (–3,2,6). %3D

A: Given that fx,y,z=ex2y+4zx3 Then  ∇f=∂∂xi+∂∂yj+∂∂zkex2y+4zx3=2xyex2y+12zx2i+x2ex2yj+4x3k

Q: Use the chain rule to find where g(u,v) = f (x(u,v),y(u,v)), f(x,y)=xy³ -4x² , ög ди x(и, у) -и*…

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Q: Find the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

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Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: f Vf(x, y) = 0, then Duf(x, y) = 0 for all u. %3D %3D

A: True

Q: dz dz Let z= f(x,y) , where x= u? + v? and y= Find and du at (u,v) = (- 40, - 4), given that :…

A: Please see the explanation below

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

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Q: Let f(x, y, z) = xy²z³ + 3 find i)f(2, 1, 3) ii)f(t, t², -t) iii)f(a + b, a – b, b)

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

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Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: If f(u,v,w)=u+v2sinw  and u=x−y, v=y−z, w=z−x find  fx+fy+fz=?

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: The gradient vector of the function f(x, y, z) = ln(yz) - x² is: Select one: ○ (−2x,, 1) O None of…

A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

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Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: Let f(x,y,z) = x2yz4 + 4xy²z+y²z - 3y³z Find fxyz

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Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: Let f(z) = kz5 + az³ + cz. Find u(x,y) if z = 3.3 + 7.8i, a = 7, c = 11, and k = 3.

A: This is a problem of complex analysis.

Q: A) f(x,y,z) = 2x + y – z , Q = {(x, y, z): 0 < x, z < 2,-2 < y< 2}

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

Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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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: C is the line segment from (-1,0, 3) to (1, 3, 4), and F(x, y, z) = zi+xj+yk, evaluate Jo F.dr.

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Q: f(x,y,z)=x+y+z and r(u,v)= (2u+ v, 3u - v, u+2v). What is the value of f(r(u,v)) r, xr, AA when u=2,…

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Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: Let F(x, y) = (2xy+ y2, x² – line from (0, 1) to (2, 3) followed by the straight line from (2, 3) to…

A: The given function is Fx,y=2xy+y-2,x2-2xy-3 and C is the straight line between the points 0,1 and…

Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

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Q: Let f(x, y, z) 48 Then Vf = and Duf(2, 1, 3) in the direction of (2, 1, 2) is

A: This is gradient of f in which take all first order partial derivatives.

Q: Consider the function f (2)= +-z Which direction is a descent direction at z (1,1)?

A: This is a problem of vector calculus.

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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Q: Let f(x,y)= x2 + xy-y2-x. Find the direction u and the value of Duf(1,1) for which Duf(1,1) kargest.…

A: Solution is given below

Q: ху af If f(x,y) then is %3D x2+y ax

A: Given function,  fx,y=xyx2+y

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2,…

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Q: Find f'(2) where f(t) = u(t) v(t), u(2) = (1,2, –1), u'(2) = (3,0, 4), and v(t) = (t, t2, t).

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Q: J f ds if Evaluate Of(x, y, z)=x+y, and C is the combinations of lines connecting adjacently the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Calculate Duf(0,–2,5) in the direction of v = -3i + 12j – 4k for the function f(x,y,z) = 3x² + xy –…

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Q: V(x,v,z)=5x² – 2xy+ xyz In which direction does V change most rapidly at P(5, 2, 4)?

A: to find the direction of maximum change we find divergence of the function. ∇v =…

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

Q: Let T : R2 → R2 given by T(x, y) = (2x + y, x − 3y), (x, y) ∈ R2. Determine [T]αα , where α = {(1,…

A: We will find the images of (1,1) and (1,2) under the linear transformation T and then write them as…

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

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Q: Let f(x,y) = x² + xy- y² – x. - x. Find the direction u and the value of Duf(1,1) for which Duf(1,1)…

A: According to question we need to find for (x,y) = (1,1) So, I am assuming there is a typo in options…

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: Determine Df(4, -1,6) for f(x, y,z) = ery +4zx in the direction of (-3,2,6).

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Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

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