Let a =i-j and b = 31 + 3/. If Daf (1,2) = 6v2 and Dof(1,2) = -2V2, then find f(1,2) and fy(1, 2)

Q: 9. If f(x, y) = x³ + 4xy² + y3 %3D show, that f (ax, ay) = a³f (x,y) %3D

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Q: A shop sells 3 brands of textile: B1, B2, and B3 of yarn, each of which is a blend of Orange (0),…

A: Given that,A shop sells 3 brands of textiles: B1, B2, and B3 of yarn, each of which is a blend of…

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: 3) If A = 2x²i – 3yzj + xz?k and ¢ = 2z – x³y, find A - Vo and A x V¢ at the point (1,-1,1). ww. 4)…

A: A=2x2 i-3yz j+xz2 kA(1,-1, 1)=(2, 3, 1)ϕ=2z-x3y∂ϕ∂x=-3x2y∂ϕ∂y=-x3∂ϕ∂z=2∇ϕ =∂ϕ∂x i +∂ϕ∂y j+∂ϕ∂z k∇ϕ…

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: Please solve

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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: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: If (x, y, z) = x²yz³ and A = xzi -y²j + 2x²yk, Determine : ww a) Ax (Vx A) at point (1,-1,1) b) VX…

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Q: If V = (3x + 2z²)i + j- (z – 7x)k then V. V at the point. (1, 1, 1) is ||

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Q: 2x+ 3y-z =1 4x + y-3z = 11 3x-2y +5z = 21 | %3D

A: Solution:

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y w = 3 5x + 2y 4 4x 2 y 5z +…

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

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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: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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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: If F(x,y,z)=x?y-y²z3 Then fz= -3y²z2

A: Given: fx, y, z=x2y3-y2z3

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: Show that A Yk= V' Yk+r

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: Use Cramer's Rule to solve x + 2y + 3z 3r + 2y +z 17 11 I- 5y +2-

A: Given: The given equations are, x+2y+3z=173x+2y+z=11x-5y+z=-5 The objective is to solve the value of…

Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=?

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

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Q: b) Find if f(x, y) = ysin( xy)

A: Givenf(x,y)=ysin(xy)find ∂w∂t

Q: Find Duf at P f(x,y,z)=4x^3y^3z^3;  P(1,−2,1);  u=1/3i+2/3j−

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Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: If fx(x)= 1/(1+x²), and fy(y)= 1/(1+y"), X & Y are independent. Find fzw(z,w), if Z-6,5 XY and…

A: Given: fxx=11+x2 fy(y)=11+y2 Determine ∂(z,w)∂(x,y)…

Q: Vy + z f(x, у, 2) 3 (а) f(1, 5, 4) (b) f(6, 7, –2)

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Q: If A = 2x2'i– yzj +3xz'k and ø=x³yz, find V×(ø4)at the point (1, 0, -1).

A: Given A = 2xz2i - yzj + 3xz3k and  ϕ = x2yzSo, ϕA=  x2yz(2xz2i - yzj + 3xz3k)     =  2x3yz3i…

Q: If f(x) = 12sin(green wave), then the red wave isni %3D 20 |-31/2 |-T1/2 T/2 3h/2 2n 5T -10

A: Solution A sinusoidal wave can be represented as f(x)=Asin(2πfx+P)..........(1) Where A is amplitude…

Q: Find fy and f, and evaluate each at the given point. (x, y, 2) = x²y³ + 2xyz – 6yz, (-2, 1, 2) ,(X,…

A: Given :- f(x, y, z) = x2 y3 +2xyz-6yz  To find:- fx(x, y, z) fy(x, y,z)  fz (x, y, z)  fx(-2,1,2)…

Q: Suppose Vf(x, y, z) = 2xyzexi + zex¯j + yex k. If f(0, 0, 0) = 1, find f(1, 3, 3). ,2 .2

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Q: Let F(x, y, z) = x² 7 + y? 3 + 3zk. Then divF(x, y, 2) is: x3 3z2 3 3 2л + 2у + 3 2x i + 2yj + 3 k…

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Q: If f(x,y)=x2+2y2, then fx(2,1) and fy(2,1) are...

A: f(x,y)=x2+2y2,find fx(2,1) and fy(2,1)

Q: Let w = iz2-4z+3i. find (a) Δw, (b) dw, (c) Δw-dw at the point z=2i

A: Consider the provided question, (a)

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: 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: on vectors for t2 0.

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Q: (a) The function z depends on u and v so that z = 2v(4- 3u)? u = 2x + 3y and v= 3x-2y az when x 0…

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Q: Solve for z using cramer's rule.  2x-y-z=4 4x+y+z=2 3y+z=2

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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: If f = ux+v-y, g=u²+vy+ w and O(f.g,h) ô(11,v, w) h= zu -v+ vw compute

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Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

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Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

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