1. Let T1,T2 : R3 → R² be given by: T1((x, y, z)) = (3x – 2y + 5z, x + 4y – 7z), and T2((x, y, z)) = (2x + 9z, x – y + 3z). %3D

Q: If f(x, y) = 4e*y cos (x- 1) , then the linear approximation at (1,0) is | (A) 4 + 16x (B) 4 + 4x…

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Q: dz Q\ let z = 8x'y-2x +3y, x = uv, y = u + v use the chain rule to find du

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Q: (b) f(x) = where A; E S™ – (det(Ao + x1A1 + ...+ xn An))/m, on {x | Ao + ¤1A1 ++xnAn > ► 0},

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Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: 1. Use the Chain Rule to find dy in terms of r. dr а у — (и—2)3 and и- 2x +1 b. y = Jū and u= 5z2 –…

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Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: dw Use an appropriate form of the chain rule to find dt w = In(10x² – 4y + 5z³); c = t', y = tỉ, z =…

A: From the given function: w=ln10x2-4y+5z3 ; x=t12 ; y=t23 ; z=t-2 As we know that: The Power law:…

Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

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Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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Q: n dy dx +P(x)y

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Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

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

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

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: Evaluate the porticalar çoution of: y(み-yty)x - x(4-y)dy %=o when x=1, y = 2 A- y?Inx + xy + x* =…

A: y(2x2+y2-xy)dx - x2(2x-y)dy = 0 dydx=y(2x2+y2-xy)x2(2x-y) dydx = (2x-y)xy + y3x2(2x-y) dydx = xyx2 +…

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: Consider h(x,y, z) = cos (xy) + eY² + In (xz) at the point P ( 1,0, = 1 Deter-

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Q: dw Use an appropriate form of the chain rule to find dt In(14.x² – 4y + 523); x = ti, y= tổ, z = t-2…

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Q: xy ) Suppose thot fixy)=e , x(4,0)= 3uSiina, glu, vl = f(x (4,v), yluiv), find , by using Chain Rule

A: Using the chain rule,

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

A: My=Nx means F is conservative vector field

Q: Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the…

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Q: FIND THE LINEARIZATION OF f(x) = 2+ [,* dt at z= 1. %3D 1+ Lütfen birini seçin: a. L(x) = 2x – 4 b.…

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Q: For all x > 0, there is a unique value y = r(x) that solves the equation y 3 +4xy = 16.(a) Show…

A: Given: The equation is: y3+4xy=16 a) We have to show that dydx=-4y(3y2+4x): Consider, y3+4xy=16…

Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: Let z = f(x, y) = e**y while x = 2st and y = s² + t³. Use a chain rule to find ôz/8t at the points…

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Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

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Q: 2 6.xy + 2z how that G(r, y, 2) = (3y? + ( 3y2 + 2x , x, y, z > 0 is conservative %3D 22 a) without…

A: Scalar potential function

Q: Consider the following. w - xy + xz + yz?, x= t, y- 7t, z-7 (a) Find dw/dt using the appropriate…

A: We have to use chain rule to solve the question.

Q: Find the Wronskian of a given set {yı, y2} of solutions of 6. y"3(x21)y- 2y 0, given that W(T) = 0.

A: Given the differential equation and the value of the wronskian at pi as:

Q: If y, (x) = e** is a solution of the D.E y" + p(x)y' + q(x)y = 0, where p(x) and q(x) are continuous…

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Q: For functions f(x,y,z) = 5xyz and g(x,y,z) = x2 + 3y? + 4z2 – 7. write the Lagrange multiplier…

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Q: 4) Find Yp, using D-operator, where Yp (e). %3D (D+1) (D-2)

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Q: 2 Let z=x ·sin(y) 2 X=S •t y= st. dz Compute & in two ways: (i) Using the chain rule and S ô t (ii)…

A: Given that , z=x2siny where x=s2t , y=st find ∂z∂s , ∂z∂t

Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: Suppose z = x² sin y, x = -s² – 21² , y = 8st. dz A. Use the chain rule to find and * as functions…

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Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: 2 Let fixy.3) = R +/y +/1 n (4-x-y-32) a. Find fi, I, 1) b of f y-j'> Fird ard des cr be the demarn…

A: a.

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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