Let D be the open unit disc in C. Lel g: D-> D be holomorphic, g() = () & let (g(2) h(z) = (s'(0) ,Z ED z+0 Which of the following are TRUR? (a) h is holomorplhic on D (b) h(1) 1 (d)

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Q: A Find T, N, and x for the space curve r(t) = (6 cos ³t) i + (6 sin ³t) j for 0 <t<. T= Di+Oj (Type…

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Compute the Jacobian of the map G(r, s) = (er cosh(s), er sinh(s))

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Q: 6. Let H := := {(x,y) = R² : y > 0}, and for (x, y) = H define x² + y²-1 -2x F(x,y) = 2…

A: 2. Show that FFF is surjective (onto)To prove that F is surjective, we need to show that for any…

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Q: 5 Thass [[1(², 3)dA = [² [² fff(x, 0 1 drdo

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Q: 1) 10 E' F' E D' D -10 10 C -10 Which rule yields the dilation of the figure CDEF centered at the…

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Q: Let f(z) := z5 . Show that f is invertible in a neighbourhood of i and calculate (f-1)'(f(i)).

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Q: Consider the function f(x,y) over the domain D enclosed by the 1+ x2 + y² polar curve r =2+…

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Q: Let P(Z)=0.46, P(Y)=0.41, and P(ZNY) = 0.19. Use a Venn diagram to find (a) P (Z'NY'), (b) P…

A: P(Z)=0.46 P(Y)=0.41 P(Z∩Y)=0.19

Q: Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b)…

A: Given Fx, y, z=x-1z, y-1z, lnxy (a) Verify for F=∇f where fx, y, z=z lnxy The gradient of a function…

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Q: a) Let f: R" → R be a function given by f(₁,₂)=1..., where = 1. Show that the maximum of f(11,…

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Q: Ex L: =)(co(ax) – 7sin(3 x)) FC<). gC<)dx Let V be the vectar real valued function of all continous…

A: An inner product space is a function from a vector space to another vector space. There are certain…

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Q: 1.T.1 Let U be the set of all twice-differentiable functions f : R → R satisfying f"(x) + 2f'(x) –…

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Q: f (x) = arctan(e“) ise ƒ '(-1) =?

A: To find the derivative of  f(x)=arctan(ex) at x=-1

Q: a) D= {(x, y)| 1<a< 2, yE R} c)D = {(x, y)| -1<e<1, 0<y< 1} e) None. b)D = {(x, y)| 1<a< 2, d)D =…

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Q: - Let f(z) = cosh z. (1) Find the image of S := {z = x+iye C: x < 0,0 < y < } under f.

A: Follow the steps.

Q: (b) Let n, m be positive integers. Define a function (2zm + 3)"e-3z sin?(z) h(z) = zm+2n cos3 (z)…

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Q: Let P(Z) = 0.42, P(Y) = 0.39, and P(ZnY) = 0.16. Use a Venn diagram to find (a) P (Z'nY'), (b)…

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Q: Let Ci be the rectangle with vertices (0,0), (2,0), (0,1), and (2,1) oriented counterclockwise, and…

A: Let C₁ be the rectangle with vertices (0,0). (2,0), (0, 1), and (2,1) oriented counterclockwise, and…