1) Let c. 1z_c)=4 and I = -82²_3 dZ. c 근림1 then Is 2IT i ?

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: 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: Find diagonal matriy D is similar with A a A = [3 8-5

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Q: 3) Show that the tangent(45°) = 1. Let "u" = 22.5°, use calculator %3D

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Q: 4/ur grans funthon y"-Uy't3y = et

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Q: 2. Show that c(x, t) = solves 1 ac(x, t) 2 ax ac(x, 1) ar

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Q: (i),if i = j + 1)',if i = B = A-, if i +j mif i + j

A: Here we have to find the Matrix A and B then find the product according to the question, now the…

Q: 3.- De la figura, calcular "a°+Bo" Bo 40° За%

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Q: .3 , Ry* In y dy

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Q: Prove az - ae that d az dz

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Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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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: 1/3 If (x+iy) =a+ ib, Prove that

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Q: 2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

A: Given The sires is convergent then,

Q: Prove inf { ñt nEN}= %3D

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

Q: 6. If u=,%) prove that xu, + yu, + zu, = 0

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Q: B) Show that coth-x = In ()

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Q: 7. If (x, y, 2) = 3xz³y – y?, find grad o at the point (1, -2, –1) Ans. - (16î + 9j + 4k)

A: The gradient of a scaler point function φ is obtained by applying the del operator ∇ to the scaler…

Q: If x, +iy,=x,+ iv, then x =y,

A: Given x1 + iy1 = x2 + iy2

Q: Hew.b prove that CAXB)-Ais atways-Zero

A: Topic:- vector  algebra

Q: Calculate x - z. (Image 24 JI 8х -2 2x +1 3z z + 22

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: lar, let m = 2 and n e of A and B such that

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Q: Prove that Vtan a de – 7//2.

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Q: 3. Show that Z, -

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Q: 4. Demonstrate that Re(iz) = -Im(z);

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Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

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Q: 12)List the first five berms of Ehe regence a,=6, aan= 5a -4 as=3 a=? asz?

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Q: iiion 125 correct to three

A: To find the approximation of (25)^1/3

Q: (4). Show that of X~UCO,!) as Y=-n-X)~ txponenkalla),

A: i) Uniform distribution : If X follows Uniform distribution over interval (a, b ) then cumulative…

Q: show that d connot be obtained from a norm.

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Q: 14) Find mzYIJ if mZHIY = 28°, %3D MZYIJ = 139x + 1, and mZHIJ= 168x. %3D Y

A: Given : m∠HIY = 28°m ∠YIJ = 139x + 1m∠HIJ = 168x

Q: Find the maaimum and miniryem Valiaes of e feencteon Cif exits) feny) Luž-3ary

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Q: Find the Reat teng th of sides of the triungle (AB Al4, 6,0), BL-6, 2,5) yclo, 9,5 ).

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Q: Prove: 4 x,,x2x, ER, then |x, +x, +.. + x,| s |x,|+|x,|+... + |x,|

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Q: and y If a = -, then æ =

A: The value of angle is  α =-π3 To evaluate : the terminal point Px,y on unit circle.

Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

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Q: I, Let dlP) S-a). End fIt) Sta

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Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

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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: (2, Prove that Ž (Pn+ Pn+1) hr 9=U (y+1) 27-²8 (14+ 2x=-1) y

A: What is Legendre Polynomial: Legendre polynomials are a set of complete and orthogonal polynomials…

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: 10- Prove that a.b3D la+bl2- la-bl? /4

A: Prove that a.b= la+bl²- la-bl²/4

Q: ul 4G . 21:29 141 , What meaning can be attached to this cross product: x j =7 O -- > Status…

A: This is a question of vector analysis

Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||

Q: Compute / (1/zy, 1/(z + y)) dr along the path from (1, 1) to (3, 1) to (3, 6) using straight line…

A: The parametric vector form of a straight line from (1,1) to (3,1) will be given by:…