Let d(x, y) = be a metric on R* then the open ball of center 2 and radius is: O ]1/2,1[ O None of the choices O 14/9,4/7[ O [4/9,4/7[

Q: v dA , R is bounded by r= 2– cose R

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Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: Let O = (0,0), and a = (2, –1) be points in R2. Set G = B (O, 1) = {v = (x, y) € R² : d2(O, v) < 1}…

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Q: p) Classify the following models as ARIMA(p,d,q). i) (1-B)x, = (1-0.3B),. ii) (1-0.5B+0.25B²)Vx, =…

A: ARIMA means auto regressive integrated moving average, It ia also written in the forn ARIMA(p,d,q)

Q: ,A, B,C be 4 points in R², no three of which colinear. Fix A' e VA, B' e VB and C' e VC h that AB ||…

A: In the following question, concept of parallel line is applied. Parallel Line Parallel lines are…

Q: Let y e R. Determine if the following are metrics on R or not: d1(x,y) = sqrt(abs(x-y))…

A: A set X and a function d together called a metric space if the function d:X×X→ℝ satisfies the…

Q: 3. This question concerns the L metric d and the L¹ metric e on a) Calculate d(f.g) and e(f.g),…

A: Consider L∞ metric d and L1metric e on C[0,1]. (i) To Find: d(f,g) , e(f,g) for  f(x)=1+x , g(x)=x2.…

Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: 2. (a) Let ds² = v du² − du dv + 2 dv². (a) Find the largest subset U of R² for which this…

A: (a) Given metric:ds2=v du2−du dv+2 dv2Comparing g11=v , g12=g21=−12 , g22=2Given metric will be…

Q: Let X = [0, 1] and d be the usual metric, d(x, y) = |x- y| %3D O True O False

A: TRUE

Q: Let X = R. and d is discrete metric, Find S (2,2) OR O (2) O {0} (2)

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Q: Q=- Find the Zero and its oider for the function fiz) = 1- Ki+Z+ ¢ ?

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Q: \si E2. is a metric on 1. Prove that d[(s), (t)] = 1=-00

A: To prove, ds,t=∑i=-∞∞si-ti2i is metric on ∑2. A metric space is a set X together with a function d…

Q: non-empty set and d:X x X R de fined by d(x,y)=31 x- 41_ 2+|xl+lyl or disprove that d is a metric on…

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Q: Let d be a metric on X + 0. Show that the function e defined by d(a, b) 1+ d(a, b) e(a, b) = %3D…

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Q: Evaluate (z* + 1)dx around the circle [z]=1 A) 0 B) 2in C2 Evaluate fx8 (2x - 1)dx A) 1 B) 0 C) -1…

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Q: = 0,1] and d be the usual metric, d(x, y) = a -y %3D en d can not induces a norm on X True False

A: the usual metric d(x,y)=|x-y| usually induces the norm.

Q: Let X=R2 and let d be the Euclidean metric.  Define d3:  R2 x R2 to R by d3(x, y) = min{1, d(x, y)}…

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnB=¢, BnC = 0, u(AnC) = 0. Determine µ(AUBUC).

A: Measure theory

Q: Let X = N and d be the usual metric, d (x, y) = |x – yl then d can induces a norm on X True O False…

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Q: 2. (i) On R², consider the metric d(x, y) = 2x1-9₁ +4₂-9₂- In this metric, sketch the closed ball B₁…

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Q: For every x, y E R, let p(x, y) = |x² – y²\. Is p a metric on R?

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Consider 2-dimensional hyperbolic space with metric ds ds'+dy and y > 0. The length of a line…

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Q: rcise 1.10. (a). Let V = R² = {(x.y)l x, y > 0} with usual addition and scalar multiplication. Is it…

A: Yes, the given set with usual addition and scalar multiplication is a vector space. Let's prove that…

Q: 38] Evaluate ∬ 40??? ? where S is the portion of y=3x2+3z2 that lies behind y=6.

A: Given The given surface integral is ∫∫S40y ds.  S is the part of y=3x2+3z2that lies behind y=6.…

Q: I need help for number 5. There are some parts in this section that I don't understand. Please give…

A: Problem 5.To prove that the given closed ball is closed.

Q: 2. Let A = d(x, y) do-metric (i.e. d»((x, a), (x', a')) = max{|x – x'|, d(a, a')}). Give examples of…

A: Discrete metric: Let X be a nonempty set. The discrete metric is defined as follows, dx,y=1 if x=y0…

Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnC = ¢, BnC = ¢, µ(An B) = 0. Determine µ(AUBUC).

A: Measure theory

Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: Let (X, B(R), ft) be a Borel measure space. ANC= 6 BOC =0 p(AnB) = 0. Determine ju(AUBUC) %3D

A: Since sets are disjoint so measure will be the sum

Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

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Q: Let F = (z,2x, y) and C is the straight segment from (0,0,0, to (1,2,2). Then F• dř = %3D a) 7/2 b)…

A: Parametrize the line and then integration.

Q: Let = (0,0), and a = (2,-1) be points in R². Set G=B¹2 (0,1)={v = (x, y) = R²: d₂(0,v) <1} H = B¹¹…

A: Let, and  be points in  SetTo find:Sketch  and The coordinates system,, and  be points in  Set

Q: Determine whether d is defined on R. Is it metric on R? d(x, y) = 13x - yl Also: if metric, show…

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