Show that in the metric space (R, 1.1), Q = 4, (Q')'=$ Cinteripr of rational numbers and interior of irational S. numbers' are empty set)

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: show that the rectaugle that has mancimum Qree for given PerimeTer is e sequare. in

A: Consider the provided question, We need to prove that the rectangle that has maximum area for a…

Q: Let (R,r) be topological space with usual topology on R, then the set Qof rationals is O Neither…

A: ℚ is the set of rational numbers. ℝ is the set of real numbers. So, ℚ is a subset of ℝ .        i.e.…

Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: 4. Find the lungth of le chord amd'its distane from the ankr. A 2.

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Q: Find the projesiin Fisi+2j intro - Scaher componet

A: The vector equation is F=5i+2j. The vector equation is v=i-3j

Q: Verify that He follow egunbin is an ielartiky Fan o -sino 2 tano

A: We will use various trigonometric formulas to answer this

Q: 15: Using first principles (by definition), prove thát thể đêrivätive of ä constant is U

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Q: every vertor (en Sination of Hhe vertars (e, 2) and {-2,1)? ☺ Is linem reitars Provida why Jatailad…

A: Solution is given by using linear independence of vectors as follows :

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Q: Find the Velumme of the Sotids abtaind Yegion in the first quadrand bound by Hhe Cerves Y=2- x² by…

A: We will draw a region first then using Integration, we will find volume of solid

Q: Prove by induetion onn that for all irdegers nz2, Nz2,Gilit)

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Q: Be M, N subsets of space W. Then span (MUN) = span (M) +span (N)- %3D

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Q: 94) Show that F= ;². ?' is Consenvatwe and gind potintial - the sealar

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Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

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: Suppose n is an integer and z-z3D =r is a contour traversed n dz %3D once in counter clockwise, then…

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Q: Find the ared of the reyion R bound ed.by and the liney=x+2 2. 2. =y-yand the line y--x ......

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Q: Dyani wrote a proof to show that ZXWY ZYZX. What is her error? Since ZWXZ LZYW, LXZW LYWZ, and XW…

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Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

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Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

Q: Prove:- The defect of a triangle in (RG) is an area function.

A: In Euclidean Geometry, the area of a triangle is calculated by multiplying the length of any side…

Q: Prove tuat fsecodo-On/sece + tanco

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Q: ☺ show dhat 2) G(x,x) => Uola) Uorlo) were G is green funcfion

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Q: Prove that $lax) =se³ is Cont. on ts don

A: Given: fx = x3 and δ≤1 To prove: f is continuous on its domain.

Q: let M= To,2] anel d be bhe usual metric then d is not compact or Compact ?

A: A set is said to be compact if and only if it is closed and bounded.

Q: Describe the largest set S on which it is correct to say that fis continuous. AX, y) = In(1 + x² +…

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Q: Suppose S, T ∈ ?(V) are such that ST = TS. Prove that range S is invariant under T.

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Q: Suppose, as a rough estimate, we say that there are 20 distinct geons used for object recognition;…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: If X = {a, b} , how many metric can be de fined on X %3D infinite O none O only one O only finite

A: only one

Q: ) Prove that sac"()/T sec

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Q: (a, b) is measurable. ulgn O ihi O

A: I will use the definition of measurable set.

Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: 2. Explain why there does not exist a measure Space (X,S, M) with the pro porty %3D

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Q: Solve the Laploce equatrons for the ondi tions flx) funciong given boundery and b elow Con dibion…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 2 la), Pu (aw by Re currence relation

A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

Q: Show that the set of all real numbers constitutes an incomplete metric space if we choose d(x, y) =…

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

Q: جليلة Let I = [= 1,₂1] ISR interval w that I is negligible Set.

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Q: Show that the set of all real number constitutes incomplete metric space an we choose doxoy) = Itan'…

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Q: 9 Find the lies which degion bounded and area in in first eyuadrant 12-axis by Jine V= n=770 Give…

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Q: Show that if ƒ′′> 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

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Q: Since, F is bounded both in LOR) and in lIR), it is Latnded in LLIR) forall fe[1,0) (Prdtem 31).

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Q: 1.Determine the line limit {an} = 37 (2cos ! en

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Q: what is a phythagoras theorem?

A: Pythagorean Theorem has a right angle triangle.

Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: 10. Prove that the set H={[,ne subgroap of GL(2, R). For show that x HxcH but xHx+H. :9 GL(2,R),

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Q: If ffinite or in finite) Contable set, thers prave that At CS}=0

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