Find the Jacobian and the Hessian of following functions; f(x,y,z) 3xy- yz + 2y z2-5xyz g(x,y,z) = xyz -x³yz + 2xy z - 5xyz %3D

Q: Q1// B: If u+v=e cos y and u-v=e'sin yfind the Jacobain of the a u, v at (x.y) (1,0) dx,y function

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Q: Use an appropriate form of the chain rule to find dz/dt 1. z = 3x?y; x = t and y = t2 2. z = 3 cos x…

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Q: Find dw/dt using the appropriate Chain Rule. Function w = x sin y x = e", y = 1 - t Value t = 0 X =…

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Q: Consider theD. E. M(x, y)dx + N(x, y)dy = 0 if M – N? = 28M, M,N, = 1 and M = 13 – N? then an…

A: Solution:-  Consider  the D.E-               M x,y  dx+Nx,y dy=0         If   My2-Nx3=28M →…

Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: 2. Given the following function f(x, y) = x3 +15x2 - 20y2 + 10. (i) Find fr. fy. frx fyy. fzy and…

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Q: Use the Chain Rule to find dz/dt if z= (x+y)e^x, x= 2− t^2, and y=t

A: Given that: z=(x+y)ex,      x=2-t2 and y=t

Q: m) dy dx C separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of…

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Q: 37. f(x, y) = e cos y at Po(0, 0), R: x ≤0.1, |y| ≤ 0.1 (Use e 1.11 and cos y ≤ 1 in estimating E.)

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Q: Inx Q1// B :- If u+v=e™ cos y and u- y=e*sin yfind the Jacobain of the alu, v) function a x, y at…

A: We have to find the Jacobian of the function ∂u, v∂x, y at the point x, y=1, 0 where u and v are…

Q: Upon multiplication by -3x¯* and using the substitution z = x¯³, dz = - 3x-ªdx, the Bernoulli's DE…

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Q: (型) y = 4 – t, z = cos x = 3t, find dz/dt using the chain rule. Assume the variables are restricted…

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Q: - 34. f(x, y) = (1/2)x² + xy + (1/4)y² + 3x − 3y + 4 at Po(2, 2), R: x2 ≤ 0.1, y - 2 ≤0.1

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Q: dz 4. a. Suppose that z = x – 3y, x = 4(t3 – 1), and y = In t. Find using the Chain Rule dt %3D dz…

A: (a) Given:- z=x3-3y2              x=4(t3-1)              y=ln tTo find:- dzdtWe first calculate dxdt…

Q: 1+x Find the approximation of S,. dx using Simpson's rule with step size h %3D 1+x2 0.25.

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Q: g(x), find dy by using Leibniz's notation for the chain rule: dx Give y = f(u) and u = dy dy du | dx…

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Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy + 2 at Po(5,2). Then find an upper…

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Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy +8 at Po(5,5). Then find an upper…

A: We have to find the linearization L(x, y) of the function f(x, y)  and then find an upper bound for…

Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x² + y? x = 5t, y = 3t t = 2 dw %3D…

A: Using chain rule

Q: 6x Find the linearization L(x,y) of the function f(x,y)= e DX cos (y) at the points (0,0) and0, The…

A: To find the linearization L(x,y) of the function f(x,y)=e6xcos(y) at the point (0,0) and (0,π2).

Q: Find the Jacobian and the Hessian of following functions; f(x,y, z) = 3xy – yz + 2y³z² – 5xyz³…

A: Here we have to find the Jacobian and Hessian of the following functions, (a) f(x,y,z) =…

Q: Determine whether the DE is exact then find the implicit solution. 3y(x²-1)dx + (x3 +8y-3x) dy=0; x…

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Q: Consider theD. E. M(x, y)dx + N(x, y)dy = 0 if M - N? = 24M, M,N, = 1 and M? = 2 - N? then an…

A: We have the differential equation Mx,ydx+Nx,ydy=0 If Nx-MyM=fy then the integrating factor is…

Q: /// 2xz dV where = {(x, y, z) | 1 < x < 4, x < y < 2æ, 0 < z < x + 3y} Evaluate E E %3D

A: We are asked to evaluate the integral.

Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: dy +y When reduced to a linear DE of order one in z, the Bernoulli's equation |=3x?y? becomes dz (A…

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Q: Given that w= x² +y³ +tª, x= siny and y =e'. Which of the following is a correct chain rule for…

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Q: Find dw/dt using the appropriate Chain Rule. w = x? + y? x = 3t, y = 10t dw dt

A: We have to solve

Q: The function f(x, y) = L(x, y) = arctan(x + 2y) can be approximated by the linear function = ax + by…

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Q: Determine if the following functions are linearly dependent or independent by determining their…

A: The Wronskian of a set of function y1, y2, y3 is defined as, If the Wronskian W is non-zero then…

Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: Consider theD. E. M(x, y)dx + N(x, y)dy = 0 %3D if M – N? = 28M, M,N, = 1 %3D %3D and M = 13 - N…

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Q: Upon multiplication by -3x-4 and using the substitution Z= X¯³, dz= - 3x-4dx, the Bernoulli's DE dx…

A: To find the equation obtained by multiplication of -3x-4 and using the substitution, z=x-3,…

Q: dV where V = dt y- x x= 2t, y = 5t, and z = t. Use the Chain Rule to find x+z' av dx (Type an…

A: Please see the explanation below

Q: Find dw/dt using the appropriate Chain Rule. Function w = x sin y x = et, y = π - t dw dt || Value t…

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Q: 4. Transform the equation y'= f(x)dx+ f(y)dy = 0. 2xy Into the form of varlable separable…

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Q: E- Use the chain rule to express dy / dx in terms of x and y: a) y=7+1 and t=2x+1 1 b) y=7+1 and x=…

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Q: Given the function y(t) with y(0) = 1,y'(0) = 3 then L(e*y") (s-1) Y(s- 1)-1 O False O True The…

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Q: dy 3. da + y = 2xy?e"

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Q: Consider theD. E. M(x, y)dx + N(x, y)dy = 0 if M - N = 24M, M,N, = 1 and M = 2 – N? then %3D %3D %3D…

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Q: Find dw/dt using the appropriate Chain Rule, Function Value w = x sin y x = e°, y = x –t t = 0 dw dt…

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Q: Consider the Bernoulli I.V.P ry'- x²y" = y, y(1) =1. where n-5. Let v= y" be the substitution that…

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Q: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

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Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: flx, v) = { xe-x(1 + y) x20 and y 2 0 otherwise rmine E(XY). ulate Cov(X, Y) and p. X, Y) =

A: Given Two components of a minicomputer have the following joint pdf for their useful lifetimes X and…

Q: Use the Chain Rule to find dz/dt. z = sin(x) cos(y),    x = The Square Root of t,    y = 8/t

A: Given: z = sin(x) cos(y),    x = √t,    y = 8/t By Chain Rule,

Q: 38. f(x, y) = ln x + ln y R: |x-1| ≤ 0.2, at Po(1, 1), y - 10.2

A: 38 Given function is fx,y=lnx+lny at P01,1. And R:x−1≤0.2, y−1≤0.2. We have to find the…

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation