5. Let f (x) R = Zz [x]/ I , = x°+1 € Z3[x] and iet where I= ( f (x) (a) Denote by 0:: 0 +1 := 1t I; anid &: = x+t. el ements of R in determint the mu W rite the terms oF ultiplicative inverse of each nOAZero element.

Q: 10 Re(1 + i)¹⁰ Select one: O a. 0 O b. 1/2 O c. 3/4 O d. 5/6

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Q: Let F(x, y) = x2 + x² + y2J- (a) Show that F. dr +| F. dr if C and C2 are the semicircular paths…

A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

Q: 2.-Determinar: E = (A – B) n (B – C) Si: A - {x/x € N / "x" es divisor de 12} B - {x/x € N/ "x" es…

A: We have to determine  E=A−B∩B−C Where, A=x|x∈N such that x is divisor of 12 B=x|x∈N such that x is…

Q: sin(32) Let f(z) and C: |z| = 1. Then ſ. ƒ(z)dz = %3D (1-2);z а. О b. Злі c. -6ni d. None of the…

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Q: Let f(x, y, z) = ln () Vxy – sin (cos (zy)) , evaluate ху %3D дх ду

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Q: Write the transformation matrix for a R2→ℝ2 linear transformation that rotates points 150∘ above the…

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Q: af Q1: a) Use the chain rule to calculate for the function f(x, y, z) = 3x² - 3y + 4xz², x =…

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Q: sin(32) Let f(z) = z²(z-m) and C: |z – n| = 1. Then f. f(z)dz = а. О b. 2ni с. -2лі d. None of the…

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Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: Gy Determin the area between the curve y= x+1 and y+x=7

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Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: 3. Let u(x, y) = e-* cos(y) and v(x, y) = (a) Show directly that the complex function f(x+iy) = u(x,…

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Q: Q2: Evaluate dw dv and w = xy + lnz , x = dw du v2 U at given values of v &u by using the chain…

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Q: Prove that A → B = (Vx)A B- (Vx)A → (Vy)B, if y is not free in B.

A: To prove that A→B ↦∀x∀A→∀yB, if y is not free in B.

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: Find u+ Hy:given that u(x,y) s tan(x+ux+ 11y") 11- x2-y?

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: sina cosa sin(a + 8) Without expanding, evaluate the determinant sin B cos B sin(ß+ 8) sin(y +8)…

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Q: Let w = x +y+ z, x = u³ + v³, y = eu, z = u – v and u = t+1, v = e*. Find the value of w (0). %3D…

A: Given: To find: The value of w'(0).

Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

Q: Compute the antiderivative using appropriate substitution. t tan-' (t“) dt 1+14 V1 – 1² + C O tan-"…

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Q: ow the processs on separating the variables of the given DE ich that all terms containing x must be…

A: Remark: A first-order differential equation is said to be separable if dy/dx = f(x, y) , the…

Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

A: Introduction :

Q: 2. The Jacobian for the change of variables z = = g(u, v), y = h(u, v) is given by Әх ду ди дv J(u,…

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Q: ( +5) Define the function F: R ²³>R by F(x,y) = { *+/+3+² of (x,y)+ (0,0) x²y²³²-34² 4 2 y O if (x,…

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Q: Let f: R² → R be defined by x3 + y3 x2 + y? if (x, y) + (0, 0) f(x, y) : if (x, y) = (0, 0).

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Q: as f(z) = e e analytic %3D

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Q: Assume you have plant defined by the transfer function G(s) = 1/(s+a). a %3D Let Y(s) = G(s)U(s)…

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Q: Let u = u(x, y, z.) be determined near (1, 1, 1) by x²y³z²u³ + 2xy²u³ - 3x³z²u=0, u(1,1,1) = 1. Find…

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Q: What is the domain of r(s) = e*i+ sj+cos sk?

A: Given: rs=esi+sj+cossk We know that for given expression domain will be domain of s and for square…