Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

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Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

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Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

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Q: 26. Approximate V50 using Ay f'(x) Ax.

A: Step ILet  y = f(x)Let ∆x be a small change in x and ∆y is correspoding change in y. As ∆x is a very…

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

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Q: 37. f(x,y) = 9-x² – 7y³; f.(3, 1), fy(3, 1)

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: u(x) = x° - 1 x = 1 at Select the correct response: O Continuous Discontinuous

A: As per guidelines we can solve only one question at a time, if you need more answer kindly repost…

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: Q2: Expand f(x, y) = [sin (x y*)] about E. 1). Q3: Given T(u) = sin (u), where u = x2 + y2, find…

A: Let's find.

Q: Find if f(x,y) = y sin xy ax %3D az Find ax if yz – In z 4. = x + y 3.

A: Given that: f(x,y)=y.sin(xy)   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: Q2: Expand f(x, y) = [sin (x y³)]? about , 1). Q3: Given T(u) = sin (u), where u = /x2 + y?, find…

A: Concept: " since you have asked multiple question, as per our guidelines we are supposed to solve…

Q: Q4) The critical points of the function f(x, y) = 8y³ – 12xy + x³ O (0,0) and (1,2) O (0,0) and…

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Q: Q3. Use fourth order Runge-Kutta with h = 1/4 to compute approximate values of y(1). y'= y(1 + e 2*…

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Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

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Q: Q4: Find fz for f(x,y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1) %3D

A: Consider the function: fx,y,z=xcosy+3z+xyz. Find fz at 1,3,-1. Since fz=∂f∂z. Calculate partial…

Q: Y : k=0 y' + (2x + 1)y = 0, rrence relation. For k > 0,

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Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: (3) Let f(x, y) = 3+sin(x) 4y2+10 Find both fa(r, y) and fy(x, y).

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Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

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Q: Use RK2 (Heun's method) with ħ = 0.5 to estimate y(1) given o: 8 Vū, y(t = 0) = 8, y' (t = 0) = 2.…

A: The Heun's method formula is The given values are h=0.5, y(0)=8, y'(0)=2 That is x0=0,y0=8 and…

Q: (8) Fs [ J" f (x, y) | бул 1 = d^Fs dyn proof (H⋅w-)

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes capabilities relying…

Q: (a) x² + zsen xyz = 0

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Q: 66. y" + 4y = f(t), y(0) = 0, y'(0) = –1, where 1, f(t) = 0, 01

A: Formula Used:L{y''}=s2Y(s)-sy(0)-y'(0)L(u(t-c) f(t-c))=e-csF(s)L(u(t-c))=e-cssL{sin…

Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: Q4: integrate the following function f(x,y) for x from z to 2n and for y from 0 to f (x, y)=…

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Q: dy when t=7. dx 13. Evaluate y = 2z' - 3z + 5 x = 4t' +t t= z' +z+1

A: Given eqn:  y=2z2-3z+5 where, dydx  at t=7 Now, dydz=4z-3x=4t3+tdtdx=112t2+1  ∴ t=z2+z+1 From the…

Q: der to evaluate t son's 1/3rd rule e used at x = 0.C of the error of

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Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: Suppos analyts s? show work. you

A: Given that f is analytic. And z≤1 And f(0)=0 And f(5)≤5 The formula for derivative is,…

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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Q: if z=0 ne function f(z)= )² if z+0 is differentiable at z= 0 LL

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Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

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Q: 6) Show that TE[f (t - a)] = e-i2mva TF[f(t)] where a e R".

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q.1 The natural domain of fur f(x,y) = lnx² + Iny is а) {(х, у):х > 0, у > 0}

A: Log function is defined for positive values

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: 2. Let f(x, y) = Vx² + y?. Find all critical points of f.

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: Q1) Evaluate SSS, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 < y < 1, 0 < z < x + y }.

A: Since you have asked multiple questions, we solve first question for you. For other question to be…