O ut pg are psimo elemanto in am intepel dmaim Rwith Limt elbment Such that P1q, thes Blow andd ą are afsoimlis. Tat

Q: Grplain why Ž diverges, 27 41 even though has a finite liniit 2 t 2

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Q: 1 Usng the eqressions for the volune and area in n-dunensond 2/2 Space givan by Vncr) 11 " and AnG)…

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Q: Ex: © Suppise that the fiowing Aransferuntin Conneclğs the lei) and (ti) coordnate Syshems; a4ス?) 2…

A: Given that, ζ=x¯1=ex1+x2x¯2=ex1-x2 To find: a) Jacobian matrix J and J-1 b) Compute J¯

Q: Pind the se Cond derivoitike of the funchen derivatıve of Chou pa (x) =

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Q: 42 ption Pran)= i?+11u +28 %3D 43-6u2-63u+392 a) lim Icm) » (w)さ Mil la s のさ uil (つ tSー

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Q: Ex: O calkulake th gui for the disanse formula in a barred cordihute system defined by R = Ax, whene…

A: Here, one matrix function, A=1-223 is given Let the X=a1b1a2b2 So, X¯=AX=a1b1a2b2.1-223…

Q: find the denivahon of the Runchon bydsing herules ofditkreohe lhon fee) = 7 %3D +260 .3 2.

A: We need to find the derivative of given function. fx=7x3-8x2-1x+250

Q: A liner tragfematin defimeed by a malrıx let IRR be a lineor tras ler malin. defneed by Tv) - Av ;…

A: I have proved Linear transformation using the definition

Q: Complete the proof that AWXY AYZW. W Y Statement Reason WZ = XY Given 1 2 YZ = WX Given 3 WY WY 4…

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Q: Suppose c is the Ciue r(t) = fay oEt zaM and F = .Evalvate ,Sint> fose O EfLaM J finds uning the…

A: Here we have to solve the line integral

Q: matoix Such that show that Let is Then detx = tt mxn

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Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

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: +(X+Z) = (X+ D DE Morgar Associativ O Distributive O Commutat .... is also

A: We will solve the problem.

Q: O Grven rref(A)=.] and A represents for mation T: R→R, Tlu)=Au. State all rectors in Show work and…

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Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: Find the second partal derkatives of the funenion Fx.y)- 2y o a6, 4y? 6x ду 6x. 4y aydx 器 4y o a 6x…

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Q: Et: let A = 13-202 07 2 6-5 -2 4 -3 5. 26084 18 Find a bosis Por 5 10 o 15 Phe null space of

A: Answer is mentioned below

Q: Show that J74) LOSK +Sinn 2. %3D TIX

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Q: Solve the fellowing differntial equetion by wsing Las lace-equat trans Br mation -3 dt +2Y3D4 wher…

A: Answer

Q: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: Conotrut a onatn'x whode Columu 8pure (leli2) & whole cli5) 10 is spanned by now &pale in Bpanned by

A: Column space is spanned by 3-dimensional vector. Row space is spanned by 2-dimensional vector.…

Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: which of the foll ow ing functinn Setisfy Rolle's conditions Frx)=1x-51 on [ 4.7]

A: We have to check that function f(x) =|x-5| is satisfy the Rolle's theorem on [4,7]

Q: c If in is an involution of X, show that (r, y)in = (yi", rin) is an involution of X12). %3D

A: Given X is a lattice. Given in  is an involution of X To show: x,yin=yin,xin is an involution of X2…

Q: 2) Find divergonce of the following functon Hoy,z) = xe ーZ ーD 472 リ+3yek

A: We will find out the required value.

Q: Queston de Which opton is cornect for the follawing serres? al lo abodely a caningeit 6) F's…

A: The given series is: ∑n=0∞ cos(nπ)6n

Q: Y is neither on the interior, nor the exte Y lies in the interior or in the exterior of Y lies on…

A: In this question we will use basic of algebra. We will use basic concept of interior angle and…

Q: Find te Turer saies onsion of the periodie fun cdon when definition of on eried are -2<tく - 5) 6くt…

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Q: Bölom 2 1) Let is be defined E= {p€ Q:2 <p^< 3}. as Show that the se t E is closed and bounded in Q.…

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Q: Shew that if f is Lip. then P is Cont. on X. Nale- In fact f is uni formly Conhnaue

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Q: #9

A: Given that the probability density function is: We have to find the probability that the call will…

Q: Decide if the statement is True or False. Justify your ans why not, and give an…

A: a) The poset (P(Z), ⊆)

Q: a. Show that T: 1² → 1² defined by Tx = y = (n), n, = r, is compact where x = (5,) and where0 <r< 1.

A: Show that T: l2→l2 defined by Tx=y=ηj, ηj=rjξj is compact where x=ξj and 0&lt;r&lt;1. Definition:…

Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: c If in is an involution of X, show that (r, y)" = (yi", xi") is an involution of X2). %3D

A: Given X is a lattice. Given in  is an involution of X To show: ((x,y)in=(yin,xin) is an involution…

Q: -Re call, Ac (Xicd) AB .bounded if JxcX,ryo Sucb that Ac BCX) A B(メイ) property (Xdl) methic space…

A: We will use the definition of compact set and bounded set to prove this property.

Q: Q1/ Prove that (Sa,0) is not Comm Sroup.

A: To prove the non commutativeness of the group

Q: Let r(t) = (5t + 2, 2t^2 − 3, 2/(1 + t^2). limt→0 r(t).

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Q: By using Cauchy Residle Theorem 到一2p 121=1

A: First we have to find residue at singular points.

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

A: Explanation of the answer is as follows

Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: Q3. Let z, y be real numbers such that ry 1 and z #y. Prove that

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Q: If x=sect and Y ztan t, evaluete at 1of the Following to %3D イット

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Q: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Q: Given: ZYLF = ZFRY, RFY AFY Prove: AFRY= AFLY Y L State ment Reason 1. ZYLF 4FRY 2. ZRFY = AFY 3. FY…

A: We have to find reasons

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.