Calc 3: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. Find Ws(7, -6) and Wt(7, -6). u(7, -6) = 4 v(7, -6) = 4 us(7, -6) = -5 vs(7, -6) = 8 ut(7, -6) = 1 vt(7, -6) = -6 Fu(4, 4) = -9 Fv(4, 4) = -2

Q: 7. State the linearization, L(r, y), of f(x, y) for the point (4, 3). f(x, y) = x3/² y Next, use the…

A: Given that  f(x,y)=x^(3/2)y  To find the linearization of f(x,y)

Q: v²u = 0, 0 < r < a, 0< z<l и (r, о) 3D f (r) и (г,1) %3 9 (г) и (а, г) %3 0

A: Given that ∇2u=0u(r,0)=f(r)u(r,l)=g(r)u(a,z)=0 Take u=R(r)Z(z) Substitute in the equation,…

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: ху f(x,y,z) =- х+у+z

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Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

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Q: 3. Find V x F for F(x, y, z) = -IZ i+ x² + y² -yz 1² + y² +√x² + y²k.

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Q: f(x, y, z) = 3x²y - 5xyz + 7yz2 2. f,(x, y, z) = f,xx, y, z) = f(x, y, z) =

A: Given query is to find the partial derivative for the given function f(x,y,z).

Q: Given f(r, y) 3z - 4ry 6y, find f-(1, y) = fu(z, y) =

A: Given f(x,y)=-3x3-4xy3-6y5

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: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: Q1. Find the linearization of f(x, y)= x² – xy + 12y? +3 at the point (3, 2).

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Q: 6) If F = (3x²y – z)i+ xz3 + y*)j – 2x³z²k, find V(V - F) at the point (2,1,0).

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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: Find V (V x F), if F(x, y, z) = 6ei+ 9xe'j - 5e k. V. (V x F) = %3D

A: Given Fx,y,z=6exzi+9xeyj-5eyzk

Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: 3 3 For the function f(x,y,z) = 5+ 7xy – 4z°, find fy, fy, and f,.

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Q: F=(x.y, x' y+3) at A=(1, 1), B=(2, –1) and C=(0, –2). %3D

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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(x,y,z)=x?y-y²z3 Then fz= -3y²z2

A: Given: fx, y, z=x2y3-y2z3

Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

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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: 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: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

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Q: х%3D1, 2, 3, Let f(x)= - otherwise a. Find G,(t). b. Use G,(t) to find V(X).

A: The probability mass function of X is, (a) The value of is,               Therefore,

Q: b. f:R² → R defined by f(x, y) = x² + y². Find f-1(0), f-'(1), and f-1(U), where U = (1,4). %3D %3D

A: Given data:     The expression of the function is: f(x,y)=x2+y2.     The expression for the inverse…

Q: Find Vf at the given point. 3 f(x,y,z) = x³ + y² − 4z² + z lnx, (1,5,3) Vf|(1,5,3)+(+()k (Simplify…

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Q: x2 If w = x".f then show that: + y², X. Wx + y. wy = nw.

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Q: f(2ecz tan z - 6z")dz=_ • tan z+z+e secz+z+e • secz-z+e - secz-z+c •- secz+z+e

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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

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Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

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Q: Given f(æ, y, z) = 6x² + 3y² + 4z², find f-(x, y, z) = | fy(x, y, 2) = | f:(x, y, z) =

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Q: OFind the linearization L (1, y) of the function f (z, y) = /176 – 4,' - 16y at %3D L (z, y) = Note:…

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Q: f (x, y) = {* - kx(x — у),0 <x< 2,-х <у<х elsewhere

A: (i) Consider the property for a joint PDF, ∫-∞∞∫-∞∞fx,ydydx=1 Substitute the values,…

Q: Lex f(z) = 22 +zim (z). If f(z) =.u(x,y) +iv(x, y), where 2+: :=xtiy, find.x (х,у) а. х2+ ху-у 2 b.…

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Q: (a) F(r, y, 2) = 7+ 27 + 3K. (b) F(r, y, 2) = i + 25 + zk. (c) F(r, y, z) = xỉ+ yj+ 3K. (d) F(r, y,…

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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: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: QY Use Gramer's Rule to Find K,y and Z -y-22 =-8 %3D 1 + 32 = 2 %3D 7X +y+Z = o

A: Craners rule used

Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 2xe³j – 3ek. - V·(V × F) =

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Q: af Let f(x, y) = 3x – y4 + 1. Find of and əx ду

A: Given : fx,y = 3x-12y4+1

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: If W[y,. y2. Y3]=0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

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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: f(x, y, z) = 4x²y - 2xyz + 9yz2 (X, y, z) = ,(x, y, z) = f_(x, y, z) =

A: Answer and explanations is given below...

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

Q: (a) F(x, y, z) = i + 27 + 3K. (b) F(r, y, 2) = i+ 25 + zk. (c) F(r, y, z) = xi+ yj+ 3K. (d) F(r, y,…

A: We have to match the vector field F to R3 and the figure labeled.

Q: f(x, y, z) = 4x²y - 8xyz + 10yz? (x, y, z) = %3D x. Y. z) = f,(x, y, z) =

A: