Find f, fy, and f. f (r, y, z) = z In (a*y® cos(2z)) f%3= fy = %3D fz =

Q: Determine the Integrating factor of the DE: y (2³e™y – 3) dæ + x (y+ x*e®v) dy = 0 -3 1

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Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (3y) at the points (0,0) and0,

A: Answer is given below

Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Find the integrating function (I. Fn.) for the reducible to exact ODE : (x-y³)dx+xy² dy = 0 а. I.Fn.…

A: Given, x-y3dx+xy2dy = 0  We have to find the integrating function (I.Fn) for the differential…

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: Find x(t) and y(t) by substitution/elimination. dx 9y + 20 cos(t) dt dy dt 10 cos(t) x – -

A: System of linear differential equation:

Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

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Q: tan(): '(), Suppose z = x = u cos(5v) , and y = u sin(5v) . Compute dz/du and az/dv in two different…

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Q: dz Find when u= 1, v=0 if z= cos(xy) – xsin(y), x= u² + v2, y= uv. dv A) 2 B -1 D) 1 E -2

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Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: S[[ 2xdV where E = {x, y, z) |0 < y < 2,0 sxs4-y²,0<= <y} E [[[ vz cos(x* kiV where E = {x, y, z)…

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Q: Show that the process X(t) = A cos At + B sin At (where A and B are RVs) is wide-sense stationary,…

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Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

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Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: f(x) = | e 'cos(af(s))ds, 0<x< 1, 0 < a < 1, -SX

A: Given: f(x)=∫01e-sxcosαf(s)ds, 0≤x≤1, 0&lt;α&lt;1

Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r

A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: The integrating factor of the linear DE dy + 5y = -9 cos x, dx is the function H(2) = e 5z Select…

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Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: Using an appropriate linearization, the local linear approximation of f() = T+ cos z at COS I is -…

A: Use linear approximation

Q: b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x,…

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Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

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Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: Find (V.VxF), where F(x, y, z) = ln xî+exyzj+tan-¹ k.

A: According to the Bartleyby guideline, only one question can be answered. Please repost another…

Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: The two functions y1(t) = sin t cos t and y2 (t) = sin 2t are linearly independent. O True False

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Q: If z + In(e³x – e + e²) = 0 %3D - find dx at the point (0, 0)

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Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: Given f(x,y) = ex cos y, Evaluate fy(2,0) O e² cos 2

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Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: Calculate dz/du and dz/dv given the following functions: 2x-y x + 3y' = f(x, y) = = Z = x(u, v) =…

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Q: The joint PDF of X and Y is given by f (x, y) = x+ 0 0 and y E (0, 1), derive E[X | Y = y] in terms…

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Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Q: Find of /dy if f(x, y) = y sin(xy) 1 + xycos(xy)csc(xy) csc(xy) B) xy cos(xy) + sin(x) A) O

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Q: In the given DE, cos x + In y + ( + ev = 0, integrating the coefficient of dx, M (x, y), with…

A: We will find the g(y) as shown below

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = , y=t, z= t'

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Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.