(b) The function f depends on u, v and t so that f(u,v,t)=u²+v+2t It is further given that (i) u=x+y-2z Calculate v=4x-2y-z x = 2t y=t² z=5 Evaluate fr. fy and f, in terms of x, y and z.

Q: If f(x,y,z)=x²y³-y²z³ Then f;= -3y²z2 Jlgn

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Q: a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain - and range of f(x, y).

A: Solution is given below..

Q: Find fa, fy, fyx and fy if f(x, y) = x + y + xy ух

A: This is second partial derivative so do the derivative like normal considering all other variable…

Q: For the function of two variables defined by ƒ(u, v) = u² cos v + v² sin u, select the option that…

A: Given: Let consider the function of two variables, f(u,v)=u2cos v+ v2 sin uWe have to find ∂f∂u…

Q: Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): =…

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Q: Consider a function of 2 variable f(x, y) = 2x³y² – 5x²y* + 3x³ – 4y³ af and Əx af Find ду

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Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

A: To solve the following

Q: Find the derivative of the function. q=V19r - r7 19 - 7,6 B)- -776 1 A)· V19r - r7 2V191 - 17 C)…

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Q: дz x² + y², x = 2x + 3t and y = s + t. Find and in two ways: Ət Let z = x дz əs (a) By Chain Rule.…

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Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: What is v(v × w)?

A: we need to find the value of

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

A:

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

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

A: Given function:To find Known facts:

Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: Let f (a, y) — 5x? — 8ӕу + 2у - fy 10х - 8y 4y -8х + 4y 10х -8х + 4у

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Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

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Q: Q2: Given the function fa) = {(2,1), (,5), (5, lo)) fo, D(f) , R(fw). Find

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Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,

Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

A: Given,