1+z+. . . . +z"= 1-zn+1 nEN, zEC, Z#1 1-z

Q: i=| .neN' JSI E (4i +1) = 2n² +3n +1 (2) i=1

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Q: 2. Prove: cot2x - csc²x = -1 %3D

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Q: vdor (2,1,3) be the {1,)1), (1, 2, >).(O, 1, 0)1 be the {ll,),l), (1, 2,3).CO,1, 0)) linear…

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Q: { 1/(x + 2) , x2, sin(x – 1)/(x – 1), x 1. y = F(x) : %3D - 2- -1 3. 6. -2- -4- -6- -8- ounan a n…

A: y=Fx=1/x+2,        x<−2x2,                  −2≤x≤1sinx−1/x−1,  x>1

Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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Q: 2 1-X ie 2=tny then prove that da

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Q: () = 2 sec(a O conon1 O pton 2

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Q: Consider the model Yi Bo +31 Xi + ui Where u = B₂Z; is unobserved. You know that 32 = 1 and you…

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Q: gorean Theorem. 12m 14m

A: Topic pythagoras Therorem

Q: alue of the pur C: |z| = (:-1)(z-

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Q: 1 the equation of th um joining (-4, 1), (

A: The latus rectum joining coordinates ,are  -4,1, 2,1. The length of latus -rectum is 4a.…

Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.

A: First we convert all expression into a+ib form then make necessary calculation.

Q: 3- Vn n=1

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Q: Prove that %3D 3 and hence. deduce that. 3--(n+3)Jn43+ (n+s)Jnes to 2.

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Q: Z1 "(cos(0, r2 Z2 02) + isin(0, – 02)](z2 # 0). 85. Let z1 = ri(cos 0, + isin 01) and z2 = r2(cos 0,…

A: Given z1=r1cosθ1+isinθ1 and z2=r2cosθ2+isinθ2.

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: defined by ф Kerф %3D (1,-1] Kerø = {i,-i} Kero = {i,1} Kerф %3D (1,-1,1, -)

A: Option (d) is correct.

Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: (W/) Express In x in terms of In x, In y, and In z. - In y + 1. In z 2 2 In x + 1 2 In x- In y + In…

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Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: 1 Integrate (i) 1+25cos x

A: We have to integrate

Q: Verify Young's Theorem z = In(2x + y) -

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Q: 3. Prove the pythagorean Theorem

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Q: 6) limSin (0 – ) 3. 2

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Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: Ai How could you prove ZC AB ZCDB? Drag tiles to the empty boxes to correctly complete the proof.…

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Q: Show using MGF technique that if Z, - N(0,1), for i = 1,2,3,4,5 , then U = Ez - x² with 5 degrees of…

A: Using the MGF technique we have to prove that : U = ∑i=15Z2i ~ χ2 with 5 degrees of freedom, If Zi ~…

Q: Prove that • I %3D

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Q: (b) State Heine-Borel Theorem.

A: (Heine-Borel Theorem). A subset A of R is compact if and only if A is bounded and closed (with…

Q: Find дхду of z = In(x² – y)

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Q: 10. Integral 2-t dt

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Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-

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Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: 23. x*y" + xy' - y = In x

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Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

A: Complex number and it's modulus

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

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Q: Ho = 0,~Po(x) = { 3 otherwise Hz = 0,~p1(x) = 1 Osxs1 O otherwise

A: It is an important part of statistics . It is widely used.

Q: Find first and second fundamenta! Texm U-V e Cos 2sin U-V of

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Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: true or false without justify The sel { 1,2,t, 3,,4,+, csx, coss is mot Ti Bomded in (CToi], Ul6)…

A: True.

Q: 2- (a) Using [X, P] = ih, show that [X, PJ = 2ih& and [&, Þ³1= 2ihP. (b) Show that [, p2 = 2in(in +…

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Q: exemple of a lineer Trans formetion I v-> V Give en thet is one to one not incertible.

A: We have to solve given problem:

Q: Consider i = (1,0,0), j= (0, 1, 0), k = (0,0, 1) and, f (x, y) = (x, ²y°, sin x, cos y, xyean +3…

A: We have to make the appropriate selection  With the help of following transformation-

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

Q: Uyy=4Uxx , U(0,y)=U(5,y)=U(x,0)=0 Uy(x,0)=3sin(2pi x)x)-2sin(5pi x), y>0

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Q: What is thie generalized union and interdection of %3D where 1-10,1)

A: As given,  λ is the index set for A.  Hence, there are two sets possible,  Aλ=0  =  [ -(1/0) ,  0]…

Q: 6) Find ôzlôu and ôzlôv if z = 5 tan (x) and x= e" + In v at the point (u,v)= (In 2,1) Ans. z, = 2,…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.