Let de and d be the Euclidean metric and Taxicab metric on R2, respectively. Show that if p, q E R², then de (p, q) ≤dt(p, q) ≤ 2. de (p, q). Conclude that a sequence in R2 converges with respect to the Euclidean metric if and only if it converges with respect to the Taxicab metric.

Q: by computing that the given funetions inde pendent on Show the are linearly indieated intorvale…

A:

Q: Let Yapp denotes the approximation of an exact value of y. Which of the following statement(s)…

A: As we know that absolute error is the difference between the actual value and the measured value. If…

Q: flx) = + %3D ) Find, ifit exists; the critical points. and the interval where' fw 5.increasing. ond…

A:

Q: Find the.local..maain.um minimum.and.Saddle ....**.. .puints.e. .... 2.

A:

Q: - . Let Zn, z be points in C and let d be the chordal metric on Co. Show that zn z → 0 if and only…

A: The answer provided below has been developed in a clear step by step manner.

Q: Find d(A) in the context of R with the standard metric when i) A = (0, 2) %3D ii) A= the set of…

A: d denotes standard metric on R which is  d(x, y) = |x-y|  , for all x, y in R.  For any non empty…

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

A:

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…

A:

Q: Let (X,d) be a metric space. For x,y ∈ X, let D(x, y) = √d(x, y). Prove that D is a metric on X.…

A:

Q: 4. i) Let X = B [a, b] and let d be the sup metric on X. If n → x in (X,d) and an is continuous at…

A:

Q: For r> 0 let A set A. = w:w= exp (¹) where 0 < |z| <r} ; determine the

A:

Q: Let X be a set, let fn : X –→ R be a sequence of functions, and let f : X → Y be a function. Let ē…

A: given let X be a set , let fn:X→ℝ be a sequence of function and let f:X→Y be a function. let ρ¯ be…

Q: The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean…

A: Note: Thank you for the question. Since multiple question with multiple sub parts are posted,…

Q: (a) In a metric space (M,d), prove that the sequence (b) = (b, b,b,...) is converge to the point b.…

A:

Q: Derive the distance formula between a point S and a plane through point P. |n· PS| d = |n|

A: We have to derive the distance formula between a point S and a plane through point P.

Q: s Show that in the metric space (R, 1.1), Q = 4, (Q')"=$ Cinterior of rational numbers and interior…

A: A rational number x is called interior point if there exists a neighbourhood of x which contains…

Q: Let X = R, and d be the diserete metrie, and A= {1,2) Show that if A is compact or not

A: Given set A={1,2}

Q: Let X be a set, let fn : X → R be a sequence of functions, and let f : X → Y be a function. Let ē…

A:

Q: Let d be a metric on X. The distance between an element p E X and a nonempt; subset AC X is defined…

A:

Q: Suppose that we define a function d that maps R2 to R by d(x,y) = { 0,. if x = y 1, if x is not…

A: Given. Let d be a function with the mapping d: R2 → R defined by, dx,y=0,  if x=y1,  if x≠y   (a) To…

Q: 5. Derive the distance formula between a point S and a plane through point P. |n PS d 3D |n|

A: Let Π be a plane passing through P with a normal vector n v is a vector parallel to n and passing…

Q: QUESTION 16 The set S=fxER:x² -4<0} with the usual metric is O A. Compact. O B. connected. OC Not…

A:

Q: Suppose E ⊂ Real Numbers. With respect to the Euclidean metric, is it possible that E' = { 1/n: n ∈…

A:

Q: Let d be a metric on X. Determine all constants k such that the following is a metric on X (a) kd…

A: Let d metric on X. Here , d satisfies following properties ,  dx , y ≥ 0  ,  ∀x , y ∈ X dx , y = dy…

Q: IJAis dense in a metric space X. then A is closed True O False O

A:

Q: Let X = R, and d be the discrete metric, and A = [3, 6) Show that if A is compact or not

A:

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

A:

Q: Prove: If ƒ e R(a) on [a,b] and g e R(a) on [a, b] , then fg e R(a) on [a,b]

A: Given if f∈Rα on a,b and g∈Rα on a,b. We have to prove that fg∈Rα on a,b. Since, f∈Rα on a,b then f…

Q: Given z1, z2 E C, define the distance between z1 and z2 by setting: d(z1, z2) := |21 – 22| . Prove…

A:

Q: . Let X be a nonempty set with metric d. Show that the function e defined by e(x, y) = min[1, d(x,…

A: We know that d(x,y) is a metric on X. Hence d satisfies all the properties of a metric.  Now e(x,y)…

Q: 13.) 2 automobiles start from the point A at the same time. One travels west at 60 miles/h and the…

A: Given Velocity of one = 60 i Velocity of second = 35 j

Q: Let X = R? , and let d2 be the usual, Euclidean metric on X. Define another metric, d : X x X → R,…

A:

Q: If x = 5 – t and y = 3 – t where t is bounded between -3 and 2, inclusively, find the following. A)…

A: Given: x=5-t2 and y=3-t where, t∈-3, 2. To find: (A) Table values and sketch the curve. (B)…

Q: Prove: If fe R(a) on [a, b] and if a <c < b, then f e R(a) on [a,c] and on [c, b] and S f da = f da…

A:

Q: For each of the following functions diR² AR²" wether I is a metric. Briefly explain [0,00) say…

A:

Q: Find the zeros of Q(x) = 5x - x² + 9 using the quadratic formula. Number of zeros: one

A: Given Quadratic formula is Q(x)=-x2+5x+9 Compare to ax2+bx+c=0 Here a=-1, b=5 and c=9.

Q: 1. Let (S, d) be a discrete metric space and p E S. Identify Sı (p), S1 (p), S2(p). 2. Let R have…

A: We will use the definition of metric function to sketch.

Q: Show that w is in span(B) and find the coordinates of w with respect to B. B = 6.

A: Linear Algebra

Q: Let [a, b] and [c, d] be intervals satisfying [c, d] C [a, b]. Show that if f E R(a) over [a, b]…

A: Given that a, b and c, d are intervals satisfying…