-. Show that both R and R2 may be covered by countably many open balls.

Q: I'm unsure of how to work a problem like this

A: We need to find a 2-degree polynomial having zeroes at

Q: Let x = {1,2, 3, 4} and P= { {},{2,3} , {43} - っ- %3D nd

A: X=1,2,3,4P=1,2,3,4

Q: Prove that the set S = {n² : n e N} is denumerable. %3D

A: We have to show that the given set S is a denumerable set.

Q: Hiw- prove that %3D

A:

Q: Find a counterexample to Lie's Theorem when k is not algebraically closed and chark = 0. %3D

A: According to Lie's theorem, for any finite-dimensional linear representation of a finite-dimensional…

Q: we divesgencatheosem to evaluate + XzK. dA cohose sisthe boundasy of cube definedd by

A: By divergence theorem we convert the given surface integral to the volume integral, and the region…

Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

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

Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: Show that S= {xER*| x < 2x.} IS convex

A:

Q: 2. Find the desivative ofy= Binx

A:

Q: find rank(AT) and nullity(A)

A: Rank of A = rank of A^T use this relation

Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: Verify that there is no magic square of order 2.

A: We will verify that there is no magic square of order 2 using the proof by contradiction.

Q: 2. Find three positive integers x, y, and z if their product is 27 and the sum is a minimum.

A: Given three positive numbers are  x, y, and z Product = xyz = 27 And sum is minimum

Q: B) Show that coth-x = In ()

A:

Q: find z trans foyms of folleing -an simwn ĭ

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Q: snip

A: Inner product of two vectors is equal to sum of product of corresponding elements of the two…

Q: Suppose S and T are balls with the same center. Show that one of them must be a subset of the other.

A: It is given that S and T are balls with same center. Let the center of the balls be a. Assume that…

Q: 10. Prove that Z has no smallest element.

A: we will prove it by contradiction, Suppose x belongs to Z  is the smallest element.

Q: Show that if x is in both W and W-, then x = 0.

A: Dot product of perpendicular vectors is 0.

Q: Prove that K4 is not outerplanar

A: In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices…

Q: Show that A° = A°-0- and A-o = A- %3D

A:

Q: prove that esch'x - In (* + x2 %3D

A:

Q: Let V and W be finite - dimensionl vecter s pace over

A:

Q: 12 २ (४) = dt | २स Prove !- \) ২-০০) = २(-०० ) 3D \

A: Given that Qx=12π∫x∞e-t22dtTo prove:1. Q-∞=12. Q-x=1-QxSolution:we know that ∫-∞∞e-x2dx=π       ...…

Q: Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0)…

A: We have to find clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the…

Q: 24. Find the Fowrier r fas - -IN X

A: Hv

Q: 4. Sketch the proph of the following funcfions; メーメ+4 (x+4 a) f(x) = (x+4) x b) gex) = %3D

A:

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

A:

Q: Determine all the number(s) c which satisfy the conclusion of Rolles Theorem for

A:

Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: find the desivalive d the functian ha)= ainfse and compute h'(2) Th o

A:

Q: Show that U. AS cuhere N= {3 unaluralnun %3D

A: To proveG={N,*} is not a group under binary operation a*b=ab where a,b∈N

Q: (X), E(Y ) EXY), Cov(X, Y) , σχ, σχ and Py.

A:

Q: 9) suppose that horx)=1, f,(x)=x ond dz(X) Prove that Ba(f, - where Ba is a Bernyterh Polymomial.

A: Given functions are f0(x)=1, f1(x)=x and f2(x)=x2 Since Bernstein polynomial is…

Q: 6. Use the IVT to prove that x2+ In r = has a solution. %3D

A: The Intermediate value theorem says: If the continuous function attains two values then it must…

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: HW.12 Describe in your own words, what is Limear tram furmatim" How the' concept of meant by n…

A: Linear Transformation:      A linear transformation of matrix is changes the original value to the…

Q: 7. Find a direct way of showing that the (2, 2)-entry of a 3 x 3 magic square with weight w must be…

A: Use the common form of 3×3 square matrix with weight w  to find (2,2) entry

Q: s convex.

A:

Q: a nonempty compact set of IR. sup Ke K. be

A:

Q: Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the…

A:

Q: Let F1 and F2 be 4-dimensional flats in R6, and suppose that F, N F, # Ø. What are the possible…

A:

Q: 2

A:

Q: Bla) 31 compute measurable

A:

Q: Find the unique fixed prbability vecter for the regular stochostic matrx A= ) 2 5 2 0 3 3

A: The following information has been given: The regular stochastic matrix is : A=311252033 We need to…

Q: Prove that any ball (open or closed or half open) in R³ is path connected.

A:

Q: 3. Prove that the sandwitch theorem.

A: