11. What theorem is used to prove that BD 1 AC? C В. D A

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: 6. In AABC, ZB = 90° and BD I AC prove that BD' = AD.DC

A:

Q: O8+ Cataulali (he volume v dune of paallelpipad detemined by The veilois 3i+2K +3k. う

A: To find the volume of a parallelepiped that is determined by the below vectors. a=i−jb=3i+2kc=−7j+3k…

Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

A:

Q: If f is Caib], ab solute maxinum continouus on then f attains valye fcc) and an ab solute mirinum an…

A: Que: Ans : Given         f(x) is any continews function on [a, b]          Let f(c)  be absolute…

Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: evaluate the in! integ ral if u = 16+ ex then e* V T6tex dx = ( Jü cu=(ile %3D

A:

Q: A B What other information is needed to prove AABCY ACDA by the HL Theorem?

A: Given : ∆ABC≅∆CDA

Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: 10. Name the theorem or postulate that lets you immediately conclude AABD ACBD. SAS ASA AAS Nore of…

A: We know that there are total four ways are available for finding two triangles congruent: SSS, or…

Q: В. Prove that A ERT ~ ASKY by SSS Similarity theorem. Statements Reasons 3 4 By Computation 15 %3D 4…

A: Given problems:-

Q: 9 IP A,Be Mnl(R) with A being nou-singular, show that (A-B) A-! CA+B) = (A+B) A! CA-B) %3D

A:

Q: D. Prove that CQ = DQ 3. In the accompanying figure we are given that se(C) = without using any part…

A: In the question we have to prove that CQ=DQ

Q: - Justify the last two steps of the proof. Given: RS UT and RT US Prove: ARST AUTS

A: Given that:

Q: Given: ZBAD = LCDA AB = CD Prove: AE = DE (HINT: Prove ABAD = ACDA first.) B 2 A D.

A: Given: The angle BAD is equal to CAD. The side AB is equal to CD. Concept used: SAS congruency rule.…

Q: Show that (hcs) de = 1 In 27 e %3D 2. 20 (ite")(2 + 1)

A: To show: ∫0ln 2e2x1+ex2ex+1dx=12ln2720. Concept used: Integration of ∫1vdv is equal to ln v+C.…

Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

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

A:

Q: 6. If y = In(r+ 1) In z then what is dy/dr? %3D

A:

Q: BC = a. Prove: AB = 2a and AC = aV3. %3D %3D

A:

Q: Prove that 12) d SIAX 13)let y=x, find Ay/Ax

A: Derivative of function

Q: 7, Prove the fallo aing theorem 18 (of sizes Such that A and B ere madrices siers addition is…

A:

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

A:

Q: af af дх ду af az and of. HINT [See Exam Find 24 fx, у, 2) : x² + y2 + z2 af af ду af az %3D

A:

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: Is S = {a + b√(2) : a, b ∈ ℤ} dense in ℝ?

A:

Q: 2. (– 13 + 3i)31

A:

Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

A:

Q: dy If then de impossible to calculate O In(æ)

A: 7.  slope of tangent line  slope at point ( 4 ,2 )

Q: 2.Prove that I (sinwt) : s2+w?

A:

Q: (3) Determine whether The following tundions are unitermly continious. Justity your answer Ca) f:…

A:

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

Q: (b) Prove or disprove that det (ABCD= det(A)det is jaett Jaet(D)

A: Let A=1111,B=1221,C=1332,D=1212 Therefore the determinants of individual matrices are: A=0,B=-3,C=-7…

Q: -Calculate the Four ier Serie for, fuay =0, -2saso %3D 2 n, Ond plat the fe-

A:

Q: 10.B.4: Suppose TE£(V) andcEF. Prove that det (cT) = cdim V det T.

A: Here given that T∈L(V),is the set of linear maps from V to V.

Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: 2. Find the exact \ength af the following curvis

A: Arc length L=∫ab1+dxdy2dy

Q: 4) Let (an) be anumsenical seguence sveh that lin u"4, Then the nadius of Comvergonce of the beries…

A: The given series is: ∑n=0∞7an2xn. We will use the root test to find the radius of convergence.

Q: 123 A=162 3 3 5 9 3 Let Calceelate Ā By Cayley- Hamil ton theorem.

A:

Q: 2! ODEV de venten egrimin yözyım alonını bulumz eksni etrafioda döndənuess te duçon

A: A=integration a to b y(t) x'(t) dt

Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

A:

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

A:

Q: 6. Given: ZR= ZZ CA= YA Prove: ACRA =AYZA Y

A:

Q: 8. Given: ON bisects LJOH, LJ = LH Prove: JN = HN JNH

A: here, in given ∆OJN and ∆OHN ∠JON=∠HON                                      ∵ ON bisect ∠JOH∠J=∠H…

Q: What is the reason for #3? Given: ZS=ZV T Prove: ASTX~AVUT Statements 1, Reasons 1, Given

A: Two angle are equal of triangle applying AA rule both triangles are congruent

Q: 15. are tag z dr z arc tag z - In /1 + z² + c – In /1 + z² + C %3D

A: By using integration by part

Q: what Reasow: Complete the proof that AHIK = AGJK. I HI I HJ GNew Givew Given K 26全CH Z GkJ Î CHKI ?…

A: angle G = angle H ( right angled angle) angle GKJ = angle HKI ( vertically opposite angle)…