5.) Set up integral the out side the cirele e

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: 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: Theorem 8o4 ŏ In a parallileguam, oppesitiangles ale equal aie

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

A:

Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: n) the Integral evalu ate car 1- (X² +3) e Xdx

A: Given integral Apply integration by parts formula to integrate

Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: Find the fowien senies fon | X), -T<X <A

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Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

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Q: An electromagnetic wave does require a medium to travel. O True O False

A:

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

A:

Q: Evaluate the integral. e3t V2 + et dt =

A: We have to find the indefinite integral

Q: Compute the integral 2u? du u² – 1

A: As per our guidelines we are supposed to answer only first question. Kindly repost other question as…

Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: is R* is contractible?

A: This is a problem of Topology.

Q: 4) Which of the following foumulas does not Kold for all x, we CZ O la wl= |2). Iw). (6) X W = ņ. W.…

A: We know that

Q: 10. Given: YX = ZX WX bisects ZYXZ Prove: AWYX AWZX

A:

Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

A:

Q: 2) Given: ZRAL E LYAL, ZRLA LYLA A Prove: AR = AY R.

A: Explained below

Q: Evaluate the integral S 3012 2/3 de using the two-point Gaussian quadrature rule. 1+16z4

A: Given integral is ∫−121221+16x4dx. We have to evaluate the given integral by using the two-point…

Q: Show that the following line integral is path independent (3,2) cosh (0,0) (8xdx+6ydy) 4.

A:

Q: Evaluate the following line integral. x-ds; C is line segment from (3,5,6) to (- 3,12,2).

A:

Q: 2.Prove that L (sinwt) %3D s2+w?

A:

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: 5. Use De Moivre's Theorem to evaluate (1 – V3i)%.

A: Demoivre's Theorem

Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

A:

Q: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: Region ¥=1=sino jn 1-st q4adrant enclosed by the eardieid

A:

Q: Evaluate the integral. | e3t V4 + et dt = %3D

A:

Q: 40. In isosceles AMNP, MN = MP. With point Q on MN, MO = QP = PN. Find mZM and mZN. Q 384.

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: 6. Given: VT bisects LSTU. ZU LS Prove: ASTV AUTV Proof: Statement

A:

Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

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: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

A:

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

A:

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

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: Show that the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

A:

Q: 7. Use Green's Theorem (and no other method) to show that the area of the triangle with vertices…

A: Greens theorem

Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

A:

Q: 2

A:

Q: s defined over ai at one point in tl асcordi

A:

Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

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

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.