- . Let Zn, z be points in C and let d be the chordal metric on Co. Show that zn z → 0 if and only if d(zn, 2)→0. Also show that if |zn| →∞ then {n} is Cauchy in Co. (Must {n} converge in C?)

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A: First, we will find the equation of a line given two points.

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A: As given that for the function y=coth-1x has verical asymptotes at x=-1 and x=1 and has horizontal…

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A: Given,          limx→∞x+45-x

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Q: If there exists open ball B (a, r) such that B (a, r) NG= Ø then a is not limit point of G True O…

A: TRUE

Q: Suppose f(z) is analytic in the unit disk D={|z| < 1} and |f(z)|<= 1 for |z| <1, Prove that…

A: Assume that f(z) is analytic on the unit disk D ={z: |z| < 1}.Also assume that |f(z)|≤1 for…

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Q: 5.] Let f : RM R be a differentiable function on u an open U of RM. a) Let [AB] be a segment…

A: Solution By StepsStep 1: Finite Increment TheoremThe finite increment theorem states that for a…

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Q: 1. Let d, be a metries on Xo and let the function a: X x XR defined be dr. y) dis. y)= prove that…

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Q: If there exists open ball B (a, r) such that B (a,r) nG = Ø then a is not limit point of G True…

A: TRUE

Q: Let and ond let F:Co, a) -R be a quactien that is and q =3 dipperenhable on Coja), and such Hhat…

A: To solve the following problem and find F(3)

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A: In the given question given that f(x) is a bounded real valued function on [a,b] then we have to…

Q: 3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: (a) Find a bijection f: (0, π) → R or prove that no such bijection exists. (b) Find a bijection g:…

A: A function f:X→Y is said to be bijective if and only if it is one one and onto That is for every…

Q: Let E be a normed space and A CE be Ā = f" c0) for giver. some continuaus Show that function f: E -…

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Q: 2/Define the topology If X-R² and T = {GK, KERZULAR} GK = {(XY) ER²|x+y >K3 Prove is topolgy on R²

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Q: Let flup be differentia ble function f x & ys Satislyng df (9,0) = 2 f (,1) = 3 J E,): -3 dy f Co,0)…

A: Question: A function fx,y satisfies f0,0=1, ∂f∂x0,0=1,∂f∂y0,0=2,∂f∂x1,1=3,∂f∂y1,1=-3 Let st is…

Q: Use Greea's Theorem ond Compute the Counter clock wise cir culotivn of É around the closed urve C .…

A:

Q: If F&) and g(x) ave combinuous on fanb] andit =5oprove thab b. b. Icefanb] Such that ffe)=gle).

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Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

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Q: On un jour owwn paper, araw n similar Set of AXes ns below. Skitch the grapin of a funchon f which…

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Q: Q4. Let A E Rnxm, n ≥ m. a) Use the SVD of A to deduce the SVD of ATA. b) If m = n and A is…

A: Given: The given expression is, A∈ℝn×m , n≥m a) To use the SVD of A to deduce the SVD of ATA b) To…

Q: Given f(x)=3x^2 + 4x + 5, determine the roots of the function. Verify them with a graph.

A: An algebraic expression is obtained by combining numbers and variables together with arithmetic…

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Q: e* , x 0 •stion Two: Discuss the continuity of f (x)

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Q: A. Show that T is a topology in X and Show that B,(x) is open set with respect to t for all r > 0

A: This is a problem of Topology.

Q: chen T:lab]-→R is pschrA? on [aib] 7 there exist a consleant Cyo St Ifw-F(8)|< C1x-y1 for all xyE…

A: First we have to show that f is uniformly continuous on [a,b]

Q: Let T be the co-finite topology on R and d0(x,y)=|x-y|. Prove that the function f:(R,T) to (R,d0)…

A: Given that T be the co-finite topology on ℝ and d0x,y=x-y To prove that the function f:ℝ,T→ℝ,d0…

Q: 1-2.11. Exercise Let In = (√n+1-√√n) and yn = (3, (-1)"). Prove or disprove that they are convergent…

A: Given That : xn=1n,n+1-nyn=(3,(-1)n) Prove or Disprove : xn, yn are convergent in the normed spaces…

Q: 3. Let fi R>R be a dipperentiabe quachon such and Fleo>7 if 2J0 the interual FCO) =d a) By using an…

A: Given that: F(x) is a differentiable function and it satisfies the following properties. F'x&gt;7…

Q: É = ( 2x3 + y°, y3 + z³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

A: We will find out the required flux.

Q: 5) Let 7 be the euclidean topology on R and 7' be the finite-closed topology on R. Define f : (R,…

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Q: Q₁: Which of the following are always true, and which one are not (for five only)? Give reason(s)…

A: Solution