2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

Q: 1-Find the gradient of (1) f (x,y)= In(x²+y²) (1,1)

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Q: 7. Compute the gradient of the following function f(x, y, z)= e-2z sin(2y) cos(2y);

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Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).

A: Must Know : Gradient function is given by ∇f=∂f∂xi+∂f∂yj+∂f∂zkGiven : f(x,y,z)=x2+y2+z2+xy+xz…

Q: b. Determine the gradient of the following function at Po h(x, y, z) = cos xy + e + In zx, Po(1, 0,…

A: We need to find gradient.

Q: Find the gradient of F(x,y,z)= (xy^2)lnz

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) %3D Vf(4, 2) =

A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

A: Topic = Functions

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

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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Q: Find the gradient of the function at the given point. f(x, y) = 3x + 5y2 + 8, (2, 1) Vf(2, 1) =

A: We have given function  fx,y=3x+5y2+8 fx=∂fx,y∂x fx=3∂x∂x+5∂y2∂x+∂8∂x fx=3+0+0 fx=3  .........(i)…

Q: Use the Chain Rule to find at aw w = x² + y² + z²; x = 10tsin s, y = 10tcos s, z = 9st² əs Find the…

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Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

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Q: Find the gradient of the function at the given point. g(x, y) = 11xe/x, (4,0) Vg(4, 0) =

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Q: Find the gradient of y = e" at the point (1, e).

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Q: 1. Determine if the gradient of the following velocity function is irrotational: V (x, y, z) = 3x³y²…

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Q: Calculate the gradient of the following function fox, y) = (x – 2)^3 sin y, at (0,0]

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Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: Find the gradient of the function f(r, h) = 2xrh + xr² at the point (2, 2). V f(2, 2) =

A: Given,   f(r,h)=2πrh+πr2

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 1, (1, 3) %3D Vf(1, 3) =

A: ∇f = <∂f/dx, df/dy> ∂f/dx = 4 df/dy = 10 y

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

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Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

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Q: find the gradients of the functions below a)f (x, y, 2) = ye* + 22 in P(0, 2, :

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Q: Find the gradient of f(x, y) =x2-5xy+y2 at the point (0, 1)

A: Gradient of the f(x,y) at a point (a,b) is given by :∇f=dfdx(a,b)i+dfdy(a,b)j

Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: a) Find the gradient of f(r, y, z) = e2= sin(2x)cos(2y)

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Q: Let f(x, y) = x² + In(2x – y). Find the gradient Vf(x, y) at the point (1, 1). O O O O

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Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

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Q: Compute the gradient Vf of the function f given by f(x, y) + y at an arbitrary point (x, y). Then…

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Q: Q. A-Find the gradient (Vf) for the following level surface at the given point: f(x, y, = x2 + y² -…

A: Given: f(x,y,z)= x2+y2-2z2+zlnx  Gradient,∇f=i∂f∂x+j∂f∂y+k∂f∂z

Q: Given f(x,y,z) = x2 + y2 + z2, find the maximum value of the directional derivative (df/ds) at the…

A: Consider the provided question,

Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: Find the gradient of z = (7x + 4y)e. Assume the variables are restricted to the domain on which the…

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Q: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) = 4i +…

A:

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 gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Q: Find the gradient of the function w = x tan( y + z), at the given point (4, 3, −1)

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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:…

Q: Find the gradient Vf for the function f(x,y)= e* sin(zy) and the directional derivative at the point…

A: to find the gradient take the partial derivatives of the function then substitute the x and y values…

Q: (е) f (х, у) %3D V2х + Зу in P(-1,2) in P(4,–2) (f) z = -1 tan y

A: We are given : f(x,y)=2x+3y in P(-1,2) Now,…

Q: (c) f(х,у) — n(x* + у?) in P(1,1) (а) z %3D ху? in Р(2, — 1)

A: Differential equations are those equations of mathematics that involve dependent variables,…

Q: 1. Consider the function f (x, y, z) = 2°y – xyzešzy Compute the gradient of f.

A: Let's find.

Q: You know that d/dt f(r(t)) = 69 at t=7 if r(t) = [t, t] and d/dt f(r(t)) = 21 at t=7 if r(t) = [t,…

A: Given that , ddtfrt=69 at t=7 if rt=t,t and ddtfrt=21 at t=7 if rt=t,14-t find the gradient of f at…

Q: Find the gradient of the function f(r, y, z) = z* In(yx), at the point (e, 1, -2) Vf(e, 1, -2) =

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Q: Find the gradient of the function at the given point. w - x tan(y + z), (8, 5, –2) Vw(8, 5, –2) =

A: