If X =R and d(x.y)30, then X metric space not metric semi metric

Q: Let d: R? x R² →R, defined as d (x, y) = |x1 - yı|+ |#2 – y2]| where x = (x1, x2), y = (y1, y2) ,…

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Q: Show that d given by d(x, y) = |x-ylis a metric on R by using definition 4.2.1. You may want to use…

A: we knew  that given metric d(x,y) = |x-y| is always ≥0.  now d(x,y) = 0 ⇔ |x-y| = 0…

Q: 1) If W = f(x, y,z) is a differentiable and x,y and z are differentiable functions of (t). By using…

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Q: Let d be metric on X, and de f ined di on X as di = max (d (r, ).0}, then dis semi metric but not…

A: Given d be an metric on X and d1 is defined on X by  d1=maxdx,y,0                     (i) To verify…

Q: Let d: R? × R² → R, defined as d (æ, y) = |æ1| where a = ("1, #2), y = (y1, 42) , then d is metric…

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Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

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Q: Let (x, y) and (z, w) be two points in R? state which of the following does not define metric on R?…

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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: Consider the following mappings on RXR: d1(x,y) = e*-Y, d2(x,y) = |2x –yl and d3(x,y) V=yl O Both d1…

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Q: 4. Show that the set of points (z, w) e C with w2 = sin z is naturally a Riemann surface. %3D

A: Let, S=z,w∈ℂ2|w2=sinz be the set in equation. The multivalued analytic function fz=sinz can be…

Q: 1. Determine which of the following function define a metric on R : (i) d(r, y) = V ly° + |x|° (ii)…

A: Metric: A metric, d on X is a function defined on X × X such that for all x, y, z ∈ X, which…

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: 4. Let r(s) be a unit speed curve with a curvature of zeroc fo. prove that the image r lies in a…

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Q: 6 cyrinder n= 4-y? bounded b n 0 dinate plane Z-y Plane L12 =2 4. ス4ーyン

A: Kindly foll

Q: Let d: Rx R R, defined as d(r, y) = 0, then d is %3D O not metric because d not sats fied d (x, y) =…

A: The correct option is the first option. i.e.  Not a metric because d does not satisfy d(x,y) = 0 iff…

Q: Compute where Cis the counter clockwise oriented boundary of upper-half unit disc D. 0.66666666667…

A: We need to find ,  ∮ y2dx + 3xydy , over  C ,  where C is the counter clockwise oriented boundary of…

Q: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: and EXPcess du dv as a function of u and v w = Xy + XZ + xz where x = u + v and y = u-v and then…

A: Use this formulas

Q: Let (x, y) and (z, w) be two points in R? state which of the following does not define metric on R2…

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Q: Exercise. a) For every ,x, y E R, let p(x, y) =| x? – y? |. Is p a metric on R? b) For every r, y E…

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Q: Let (x, y) and (z, w) be two points in R? state which of the following does not define metric on R?…

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Q: hy sphere x + y +z = 25 between planes z=2 and z= 4.

A: We need to find surface area using double intergral.

Q: Suppose d is Show that p: X?> [0,00) defined by a metric on X, p Cxy)= 3d (x,y) %3D 2+3d(x, u) is…

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Q: (b) Let X = {r € R: -1 <1<0or 0 <1< 1} with the usual metric.Then X is disconnected.

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Q: (10) Define the metric d on R² by d( (x₁, y₁), (x2, y2)) = max{ |x₁ − x2\,|y₁ - y2|}. Verify that…

A: The given problem is to verify that the given metric d on R2. Given metric…

Q: Let X = R and x, y E R. Admit for all x and y the metric d(x, y) = |arctan x arctan y|. | Compare…

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Q: O If and exist in a neighborhod of (a, b) and are continuous at (a, b) then f(x, y) is…

A: This is a problem of multivariable calculus.

Q: Evaluate w at x =y=Z=l if w= (os(uv) u= Xy Z and V = %3D %3D

A: Consider the given function:

Q: 8. f(x, y) = R is the disk x +y < 9. %3D x² + y? + 1' 1. 1.

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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Evaluate J CurIF. [cariF- nas F(x,v,z) = - yi + xj + zk, and S is part of the sphere z =9-x2 - y?…

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Q: Let d(x,y) = |1/x - 1/yl be a metric on RI(0}XRI(O}. Then the open ball of center 1/2 and radius 1/3…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and…

A: The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a…

Q: Question 4. Prove that the metrics defined on R? with the following rules; 1/2 de (x, y) = E (Tk –…

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Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

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Q: ) Let z(x, y) = x" be a function defined on a disk D in the positive quadrant the point (1, 2).…

A: As per the question we are given a bivariate function : z(x,y) = xy Defined on a disc D containing…

Q: d(r, y) 1+d(x,y) 5. Let (X, d) be a metric space. Define f : X x X → R by f(r, y) = Show that f is a…

A: (χ , d)  be a metric space , define f :χ×χ→ℝ by f(x , y)=d(x , y)1+d(x , y) Positive definite…

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x? +…

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Q: Let d(x.y) = |1/x - 1/y be a metric on R(0)XR\(0). Then the open ball of center 1 and radius 1/4 is*…

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Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

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Q: Let X = R², x, y EX where x = (x₁, x2), y = (y₁.Y2) with the metric function (4 pts) (x, y) =…

A: This is a question of topology and metric space.

Q: =) Veaity gren's theorem fintegral So (zy'tat 3ndy) bound ay of dosed and y-m to evaluale line whee…

A: Firstly we use green's theorem to calculate the integral. ∫P dx+Q dy=∫∫RQx-Pydy dx∫2y2 dx+3x…