1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( – i)

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

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Q: O Discuss he Singularities and Paks ZE Sinz (--2)(Z²-)}(Z"+ SZ+6)(2+7)(214)

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Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* - 6x – 2y² + 1 (Express numbers…

A: Given function f(x,y)=x3+y4-6x-2y2+1

Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: af 7. Compute and дхду a²f : f(x, y)=x'y² – sin 2 + xe" - əx' əy

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Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: 4- Find Y/dz If x²(x- y)? = x² - y? dyla

A: Find the derivative

Q: If (x, y) > (x+3, y-7) maps TUVW to T'U'V'W', what is the algebraic description that will map…

A: x, y→x+3, y-7 maps TUVW to T'U'V'W'. That is, the x-coordinates of T, U, V and W are added by 3…

Q: Q4- Given y = u2-1 and u = Vx2 +2 find y u2+1

A: Consider the equation On finding the derivative with respect to u

Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

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Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: 14 11 " f(2)da - /" f(=)dz = [ f(=)dz where a = and b = Question Help: D Post to forum

A: Let's find.

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers…

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Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: Si se sabe que L {y"(t)} = -18s + 22 con y(0) = -13 y y' (0) = 3, entonces se puede asegurar que:…

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Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: You hare shown that e jul dw or , erchenying w and t Jlw) = Use a chume of veriables to genenle…

A: Consider the given information: δ(t)=12π∫-ωωejωtdω                  ..(1) δ(ω)=12π∫-ωωejωtdt…

Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Thene m for Voritly functiom Mean Valne fex) 2. 3X -4 +S the

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x-2y² + 2 (Express numbers in…

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Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

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Q: O show thet fu) =2a +3b is Candin Uous where a, b are Constants.

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Q: 2.) Use the chain cule to find dz and d ond guen the fllowng: Yoy must show in work that your the…

A: We have to find partial derivatives.  Concept:

Q: e-", if 0 3,

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

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Q: 6. Consider the following model: Yi = Bo+B,D11 + B2D21 +u; O if person i is a non-immigrant) where…

A: Dummy Variable Trap: It is defined as the scenario when the attributes are highly correlted. One…

Q: (b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so O on the interval [2, 4] and v(t) > v %3|…

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: II. If x? + y? – 4x + 4y = 27, find expressions for and in terms of x and y, dx dy dx dx2…

A: Ans:- 5/6 &amp; -55/216 For detail...go through the solution

Q: (:)--] (b) L: R² → R* defined by L()-" -u2 (a) L: R2 → R² defined by L U2 uj + ku2 U2 u2 (c) L: R3 →…

A: We have to find the standard matrix representing each given linear transformation.

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…

Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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