What is the rule for the reflection? B. O fy-x(x, y) → (-y, -x) O Ty-x(x, y) → (-y,-x) O ry-x(X, y) - (V, x) O ry=-x(X, y) → (y, x) -2 -2A' B' C' 2. A

Q: 19. f(x, y) = x + y+y+ 1, constrained to the triangle with vertices (0, 1), (-1,–1) and (1, +1). %3D

A: As per bartleby guidelines i can answer only one question, kinldy upload rest questions separately.…

Q: aw If w = (x+y + z)2, x = r-s, y = cos(r + s), z = sin(r + s) then where r = 1, s = -1 ar using…

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Q: Use the chain rule to find where g(u,v) = f (x(u,v),y(u,v)), f(x,y)=xy³ -4x² , ög ди x(и, у) -и*…

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Q: FK - R, d(P, P3) = max {|x1 – zal. In – valj, Pa (21.), Pz= (2. 92) 4 the the mapping T(z,y) = (I,…

A: Let (x1, y1), (x2, y2)∈ℝ2 Then T1(x1, y1)=(23x1, 45y1)T2(x2, y2)=(23x2, 45y2) Let…

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: Let u (x, y) = 3x?y+2x2- y³ –2y². Then the harmonic conjugate is a. v(x, y)=x³ – 3y²x+4y²x+ C b.…

A: Harmonic conjugate of the given function

Q: Verify that ) Determine from y Graph the solition of the IVP. is a solution of the ODE. . the…

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Q: Q2:- Evaluate / x + ydA where Ris the trapezoidal region with vertices given by R 5 5 (0,0), (5, 0).…

A: To find - Evaluate ∬Rx + y dA where R is the trapezoidal region with vertices given by…

Q: Ôz and Show 4. Use an appropriate form of the chain rule to find dv (a) z3x²-y tanx, x =u/v, y = u'v

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Q: Given the transformations, which one is linear?   (a) T: R2 → R3, T(x, y) = (x - y, 3x - 2y) (b) T:…

A: Consider a transformation T :ℝn → ℝm is Linear if(i)  T(u+v)=T(u) +T(v)(ii) T(αu)  =αT(u) for all…

Q: 7. Find the Jacobian of the transformation T(x, y) = (w sin(v²),w cos(v²)). X=w Sin (v?) w = sin…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question (Q7) for you.…

Q: BCs: u(0, t) =u (I, t) = 0, t>0 ICs: u (x, 0) = ƒ(x), u,(x, 0) = 0,

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Q: Find the linearization L (x, y) of the function f (x, y) = y/-x at (-9,4). 2 L(x, y) -x+ 3y – 6 3…

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Q: 17-22 Use appropriate forms of the chain rule to find ðz/du and Əz/dv. 17. z = &x?y – 2r + 3y; x=…

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Q: Q Q 18. What is the rule for this reflection? -6 -5 4 -3 -2 OI 2 3 4 $ 6 -1- F ) (2, y) → (-2, y) O…

A: Here, we have to find the rule for the given reflection.

Q: e the Chain Rule to evaluate hu and u when w = xz+yz - z, x = uv, y= uv, and z = u and (u, v) = (1,…

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Q: Find (T3 T2 T1)¯1 if T (x,y, z) = (x – y, - y, x+ z) T2(x,y, z) = (x - y + z, 0, 3x) T3 (x, y, z) =…

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Q: The notation (x, y) (y, x) defines a reflection in the coordinate plane. O True O False QuickNa

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Q: dz 9-1f r= √x² + y², u= y² - 4x ,z = sinxy then ****, using jacobian? 0.23 O -0.25 O Non of the…

A: Given that, r=x2+y2, u=y2-4x, z=sinxy Find the value of ∂z∂u0,1,1 by using the Jacobian. Using the…

Q: Find the Jacobian for the indicated change of variables. x = uy -2u, y = uv О д(x,y) H(u, v) О…

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Q: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: ( w"-y+ (x+ ¥)'y = In (금 + z) y(-}) = 1, y' (-}) = o %3D

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Q: 비 az and Given that z = e*, x= 2u+ v, y= .y==. Find using the chain rule. au

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Q: Q2 Let C be the line segment joining the origin and the point (2,0, 1) and C2 be the line segment…

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Q: Q2- By using Chain Rule, find au/ax, du/dy, du/əz at (x, y, z) = (√√3, 2, 1) P-q u= p=x+y+z q=x-y+z,…

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Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: (b) Find fx, fy and f,if f(x,y,z) = zln(x²ycosz). (c) Use chain rule to find du and 2 if z =;x =…

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Q: 4 sin(5xy) Let f(x, y, z) : %3D Find the linearization L(x, y, z) of f(x, y, z) at the point (7, ,…

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Q: Write the chain rule for- at aw given that w = f(x,y,z); x = g(t), y = h(r,t), z = k(s,t)

A: We are given that w = f(x, y, z), x = g(t), y = h(r, t), and z = k(s, t). We need to write the chain…

Q: 1 reflection across y 2 A) X(2, 1), Y(4, 4), w(0, 5) B) X(0, 3), Y(-2, 0), w(2, –1) C) x(2, 3), Y(0,…

A: Topic:- reflection about given axis

Q: 4) reflection across x = 2 A) Y(3, 3), x(-1, 1), z(3, –2) B) Y(5, 3), X(1, 1), z(5, -2) C) Y(1, 3),…

A: We can find the  coordinate for each transformation as below

Q: Find the Jacobian d(x,y,z)/ d(u,v,w) of the transformations below. a. x = u cos v, y = 4u sin v, z…

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Q: (1) Determine the Jacobian ôx/ôq for the following system: x= [u, v, w], q = [x, y, AJ. u = x + 3y…

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

Q: -) reflection across the x-axis A) D(-5, –3), E(-5, 2), F'(-2, 1) B) E(4, 5), F'(1, 4), D(4, 0) C)…

A: NOTE: Refresh your page if you can't see any equations. . here coordinates of the given triangle…

Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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Q: Evaluate R CF. dr with F(x, y, z)=(x2 + y)i – (3xz)j + (z – 4y) k, with the path C as the line…

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Q: %3D iv) if zy = (x)- then zz + Zy = %3D 2

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Q: Given that the system xy + zu + v? x'z + 2y- uv = 3 = 2 хи + yu - хуz = 1 can be solved for x, y,…

A: Consider the given system of equations.

Q: In Exercises 9-20, use the Chain Rule to calculate - f(r(t)) at the value dt of t given.

A: NOTE : As per Bartleby guidelines, incase of multiple questions only one will be answered. Please…

Q: 22. Find the Jacobian ô(x, y, z)/a(u, v, w) of the transformation а. х 3D и соs v, у 3D u sin v, b.…

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Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t.) z =…

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Q: 2. Let u(x, y) = 2+ 3.x – y + x² – y? – 4.xy. Show that u(x, y) is harmonic and find the harmonic…

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Q: Əw/əs and əw/ət by using the appropriate Chain Rule. w = x cos yz, x = s², y = t², z = s - 5t

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Q: az Use the Chain Rule to find at for z = In(x? + y), x = st, y = t/s.

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: glx, y) =y la (xy) Deteremine the Ist and end deg nee polynomi al appreximations, L lxx) and Qla,y)…

A: Please refer to the image below

Q: -52 +1 -3 If zo =-1, G(z) = and f (y) = -5 y1 4 - 2 y2 Y3 + v -4 y1 - 2 32, find the Jacobian of G…

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Q: 1) Given the mapping F(x,y,z)=(3e" ,xzsin 2y ,xy), v=(2,2,-1), using the definition, then the…

A: Let p be a point in ℝn and F:ℝn→ℝm be a map, then the tangent map of F at p is a map between the…

Q: Given w = f(x, y, z), x = g1(r, s), y = g2(r, s), and z = 93(r, s), write the chain rule for ow and…

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Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: 4. Choose the one-parameter family that corresponds to each bifurcation diagram below. Briefly state…

A: [I]  dydt=Ay-y2 Equilibrium point Ay-y2=0  ⇒y=0, y=A fy=Ay-y2f'y=A-2yf'0=A,…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.