The value of W (x, x², x³) is

Q: a²f af af and əx' əy :f(x, y) = (x+ y)(2x + y)² Compute se дхду

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Q: Show that if F = xi + yj + zk, then ∇ * F = 0.

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Q: Find fx and fy, and evaluate at the given point.

A: The given function is: fx, y=xyx-y and the point is 2, -2. To find the fx and fy, first…

Q: I. If g(x) = Vx – 4 and h(x) = x³ + 4 , find (hog)(x) %3D

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Q: If z = x + iy, z/3 – a – ib and * = 2 (a' -b'), then a is equal а b y to

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Q: Given f(x, y, z) = v- 5x – 3y – 4z, find fa(x, Y, z) = f,(x, y, z) = f:(x, y, z) =

A: Given,          fx,y,z=-5x-3y-4z

Q: Given f(x, y, z) = 2e(z+y), Find fy(0,},-4).

A: here we have to find partial derivative of a function w.r.t. 'y' and here we also use chain rule.

Q: then E(y) and V(y) are

A: here given , y =  5x-1  E(x) = 2,  v(x) = 1

Q: Given f(x,y)= x^6 - 5x^2y^2+2y^4, find fxy(x,y)

A: By using partial differential property

Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D 4.

A: We will find the dimension of W

Q: Find f, f, and f,, and evaluate each at the given point. y' Z' 2,3 f(x, y, z) = x'y° + 2xyz – 8yz,…

A: Given   f(x,y,z)=x2y3+2xyz-8yz

Q: If fó f(x)dx = n , f, 79(x) dx : 7, and g(x) dx = 2, what is the value of S, g(x) dx?

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Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

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Q: Given f(x, y) = 6,/3x* + 5y + 4xy°, find f-(2, y) = %3D fy(x, y) = %3D

A: Solution:

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

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Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (c) z = x2 + 2y2 ; x = es - et, y = es + et

A: Formula to find the partial derivatives helps to find the partial derivatives of the function with…

Q: Find fx, fy, and fz, and evaluate each at the given point.…

A: We have to find fx,fy and fz for a given function fx,y,z=x3yz2 and also we have to evalute fx,fy and…

Q: The discriminant of ax? + bx +c = 0 is defined by-

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Q: Given w = f(x, Y, z) =

A: Given,                                   w=f(x, y, z)=4x2+y2+4z2and…

Q: Obtain (i) P (X 1)

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Q: Find x, y, z, and w. x 5 (2x - 1) ")- (2x – 3) y 4 4y (w + 1) (3y + 7) X = y = z = W =

A: Two matrices are equivalent when the corresponding terms of the matrices are equal.

Q: If f(u) : f'(u) = V13 + w'dw then

A: Let,

Q: The div A at p(1,1,2) for A is .... Å = x²y i + 2 x z j + 4 - z² y k - 3 ( 3 зі зј о

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Q: Let x be a c.r.v., the E(x4) can be founded by xf(x) dx. O True False

A: Given problem Given that   Let x be a c.r.v., the E( x4 ) can be bounded by ∫-∞∞xf(x) dx   Ans)…

Q: If Z = x.n. f (), then show that: x. Zx + y.Zy = z

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Q: The value of a that makes the given fuction continous fx)=Sx -2 x22; x)~lax²+2x<2 3 3 2 2.

A: A function f(x) is continuous at x=a if the left-hand limit, the right-hand limit, and the values of…

Q: : Given a r.v.*=2, 3,4,5, then Find the Pif. of X (fw): ,

A: Given that, a  random variable , X = 1,2,3,4,5 We need to find probability function of X i.e f(x)

Q: Find and a and дхду f(x,y) = x2 - y2 + 6xy + 4x – 8y + 2 a. b. f(x, y) = e*y + xy

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Q: Find fx, fy, and fz, and evaluate each at the given point.…

A: the given function is: fx,y,z=xyx+y+z the given point is (3,1,-1) we have to find fx, fy and fz and…

Q: Given 7 = f (x. y)= e² , when x(u,v) = 3usin(v) and y(u,v)=8v²u, Find f„(x,y) and f,(x,y)

A: Given function is: f(x,y)=e2xyx=3usinv;  y=8v2u Substitute values of 'x' and 'y' in the given…

Q: Find x, y, z, and w. x 2 (2x - 1) (2x - 2) y 7 3y (w + 1) (2y + + 3) y = = M x N W

A: Given:x22x-1y73y=2x-2z33w+12y+3

Q: Find the value of w and Х. 18 a) w= 1 x= 2 b) w 2, x 17 %3D c) w 3, x 15 %3D %3D d) w 2, x = 18 e) w…

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Q: Given f(x, y) = – 5x + 6xy° + 3y, find - fa(z, y) = %3D f,(z, y) = !!

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Q: If f(x, y) 3D х'у? — 2x'y + 3х, find (а) f.(x, у) and f,(х, у), (b) f:(2 , –1) and f;(2 , –1)

A: To find partial derivatives of f(x,y) = x3y2 - 2x2y + 3x To find :- (a)fx(x,y) and fy(x,y)…

Q: If F (x, y, z) = e^xz i + 3xe^y j − e^yz k, then find ∇.(∇ × F)

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Q: Find f, and f, for f(x, y) = 11(2x – 6y + 5)*. fx (x.y) =D

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Q: If C is given by x = 2t, y = −2t, z = t, 0 ≤ t ≤ 2, evaluate Z C (x − y + z) ds

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Q: wx + yz = bc, for z II

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Q: Find fx, fy, and fz, and evaluate each at the given point.                                     f(x,…

A: the given function is: fx,y,z=ln xyz the given point is (1,-1,-1) we have to find fx, fy and fz and…

Q: Evaluate G(x,y)dy , if Gx.y)=2xy ,x 5cost ,y 5sint ,0stsm/3.

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Q: Find f, and f and evaluate each at the given point. 2xy KX, y) = + 2y (1, 1) ,(X, y) = F,(1, 1) =…

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: The joint pmf of X and Y are given in the table below: Y X 2 4 2 1 15 15 3 15 3 15 15 23

A: Here we have to find the expectation of E(x) from given joint pmf table 3/

Q: x2 If w = x" . fG x²+ y². %3D then show that: X. Wx + y. wy = nw.

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