E) If F(x, y, z) = 3x²i + 3zj-3xk

Q: ) Consider the functions f(x) = (x + 3)² and g(x)=√x a.) Find fo g(9) 13 9(9) = √5 = 8(3) =(3+3) ²…

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Q: b) Compute Re fli) when: $(2) = √2-₁² and f(0) = -i

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Q: By using the substitution u = 4x +1, evaluate (4x + 1) dx %3D

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Q: Find (a) u x v, (b) v x u, and (c) v x v.

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Q: Transform ϕ (xmyn) ydx + ψ(xmyn) xdy = 0 to the type variables separable by the substitution z =…

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Q: if y = 3x² – 4r³ + 3ª + VI + a, then dy/dr is:

A: Given that     y = 3x2-4x5+3x+√x+π Here we have to find dy/dx . We know that        dxn/dx = nxn-1…

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: V(A - B) = A x (V x B) + B x (V x A) + (A - V)B + (B V)A,

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Q: Calculate (x+y+z) ds

A: In this question, we evaluate the surface integral for the given intersection of the curves.

Q: Show that the equation (1, 2, 3) × v = (−1, 2, a) has no solutionfor a = −1

A: Consider the given: Given equation:1,2,3×v=−1,2,aLet v=x,y,z1,2,3×v=ijk123xyz…

Q: Find x and y given that (x+yi)/2+i = (1-i)/2+3i

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Q: Find x, y, z, and w. x 8 (2x- 1) (2x - 3) 7y (w + 1) (6y + 5) X = y =

A: Given x82x-1y67y=2x-3z55w+16y+5.

Q: Use Cramer's rule find yhe solution of x1: 2x1+X2-3x3=0 4x1+5x2+X3=8 -2x1-x+4x3=2

A: write the matrix D from the given equations  D=21-3451-2-14 calculate the determinant D…

Q: Transform ϕ (xmyn) ydx + ψ (xmyn) xdy = 0 to the type variables separable by the substitution z =…

A: Given differential equation is 2+4x2+yydx+x3ydy=0......1. Compare equation 1 with Mdx+Ndy=0, we get…

Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

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Q: Evalute ) (2xty)dA, where D=2C2-1にと」 225y41tX)

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Q: Express in the form of x + iy: 6-7i (i) 5+i 1 + (3+i)2 1 (ii) (3-i)2

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Q: Find a such that the distance from (−1, 2) to ax − y + 9 = 0 is √5 units.

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Q: For f(r, v) = + find f(3,4) and state the domain of S(1, y).

A: We are given the two variable function here. To find the value f(3,4) we will simply put x=3 and…

Q: For two points (x1, y1) and  (x2, y2) such that xi > 0, yi > 0 for i = 1, 2, we say  (x2,…

A: There are about 4 functions provided.To show:They are Schur convex or not.Concept used:i) Any…

Q: ) fx)= 3x"+会

A:

Q: Soly

A: Given  u = ( -1 , 0, 1, 1)   v = ( 2, 3, -1, 0)

Q: Evaluate [ T 1-x² x² + y² dydx.

A: Given: The integral is ∫022∫x1-x2x2+y2dydx. The aim is to evaluate the given integral. Concept:  The…

Q: and こ=< ,フ-<o,-1y. where %3D Pind マf(2)?

A:

Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: 1) Find whether the signals are memoryless or memory? a) y(t) = 5x2(t+2) b) w(t) = (t-9)x(t)

A: a) Given signal is: yt=5x2t+2 Substitute: t=1. y1=5x21+2y1=5x23 So, the output at t=1 depends upon…

Q: Given that fx) = 2r-3 and g(r) = 9x²-5x+11, determine the following: a. g(x) – Ax) = b. flx) • g(x)…

A: Given that…

Q: If 2x = xy + y2, then A. C. -2 + y x + 2y (2-y) x + 2y dx 11 B. D. -(2 + y) x + 2y -(-2+ y) x + 2xy

A: