3) Use the Second Principle of Finite I nduction to establish that for all nz I o"-1= (a-1) Co to ta 7-3 ttot) %3D LHint: antt -1=(at!) ca^aD-acon-).]

Q: E valugte the cube raot of z when 2=27 Cis(210) ( Let 0s GS360°) Smallost ☺ ualus) targonst ualue).

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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

A: Given : ∆ABC≅∆CDA

Q: 2. Use Cauchy- show that each of these funedioca is. nowhere analati -Rlemman.cqmtione to bfi27=2xyi

A: Nowhere Analytic functions

Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: Suppose that > ak = a and let c E R. Prove, in all the that (c-an) = gory detail necessary, = c•Q.…

A: We will give two proofs one based on partial sums and the other will be a direct proof.

Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

A:

Q: 1. Identify which theorem will prove that ZEDC = ZDEC= ZECD if DE EC = CD. A,

A: Given problem:-

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: 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: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: 2. Which piece of information is necessary to use the SSS Congruence Postulate to prove that ATRY Y…

A: Which piece of information is necessary to use the SSS Congruence Postulate to prove that ΔTRY≅ΔCAP,…

Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: is a conplex saries of nunbers and for VNEN monert an, bn ER Let 2n- an +ibn. Show that if Ź 2n =…

A: Given:  ∑n=1∞zn is a complex series of numbers and  ∀n∈ℕ, an , bn∈ℝ Let zn= an+i bn To show that :…

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

A:

Q: sent that by a positiv ntity N(0) is 2.

A: Given as, dNdt=?N0=?

Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

A:

Q: Let C be the shortest path that connects z to ri and /= J, (sinhz + 1)dz. Then O 1 cosh r+ n(1+) O…

A:

Q: V218 in 7 in 13 in No, the relationship of the sides DOES NOT follow Pythagorean Theorem No, the…

A: Using Pythagorean theorem,

Q: 4. In the diagram below, Ĝl is parallel to NT, and IN intersects GT at A. Prove: AGIA~ATNA

A: Given :GI is parallel to NT

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

A:

Q: (- For all asb,C EZ,prove the folloNing (i)ala,1la, andal0; (ii)0la if and only if a=0; (iit)alb ond…

A:

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

A:

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

A:

Q: 2. (– 13 + 3i)31

A:

Q: (o, 1,) 1. find th directional denivatve in the dire chons of at 2 Gve inter pretahon of amp uted…

A:

Q: ) Let z be a c complese number then cos ( 58+2) is bounded in C2

A: Since, sinz and cosz are unbounded on C. These are unbounded along horizontal axis .

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

A:

Q: Consider the fune tion fa)- In[ax- b an tb] where c= ? -6 bi 2ab ind f' ()

A:

Q: Show that every positive sol fron of Ay + B, k=osl,2- & bosunded, %3D JK is i-e, ogy sB-if A<1. 1-A

A: Given yk+1=Ayk+B, k=0,1,2,... Then the objective is to find the solution at which the sequence is…

Q: 1. In the figure, E is the midpoint of (NS)¯and LSzZN. Which postulate justifies that APES = A MEN?…

A: Introduction: When two parallel lines are intersected by a transversal, the pair of angles formed on…

Q: Ex: @ write out the expessien R(n=4) jki in full. wuich aue free and which ane dummy indices ?…

A: We write expression of curvature Tensor

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: 7. Let B =- and = are bases for R? %3D

A:

Q: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

Q: 3) Prove There exists a real nubrsSo Surh thot

A:

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

A:

Q: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: Prove the following: 7. Given: PS bisects ZRST, 2SP = 3SQ, 2ST = 3SR T. Prove: ASTP~ASRQ

A: topic - similar triangles

Q: Prove that (i) Res (tan z, r/2) = - 1

A: Here,we have to prove that Res(tanz,pi/2)=-1

Q: AB is tangent te OC at point A. mod

A: Given : AB is tangent to the circle at the point A. ∠ABC = 37°

Q: Select all the Points through which a unique solution for the DE ,2 y? IS nySot eed by the Existence…

A: Given differential equation is y'=13-x2-y2

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: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

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: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A:

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)…