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Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

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Q: Let z be a complex mumber o B19) s and c be any then So BlE)dz+a fle) dz isequi contou any funckon…

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Q: 2. Consider the following quadratic form; F(x,y) = ax? +2bxy + cy. Examine under which conditions on…

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Q: 2. Solve the following Cauchy problem: Uu = Uzz -0 0, u(x,0) = x – a², u(x,0) = 4x, -00 <x < 0. %3D

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Q: Ex(30) and fYx show that of - Ix Exlz0)& Lekf:Xy be fIxYbe be it is

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: Since D is a square whose vertices have coordinates (0,0), (0,1), (1,0) and (1,1), which of the…

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Q: In a cubic spline approximation assume that we know that S;(x) = 3 + 2x - x2 + 4x3 S+1(x) = a + bx +…

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Q: (c) Prove that 1, have equal roots if e= a'm +b °

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Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0,…

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Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

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Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: Drag the postulate or theorem that proves the trieng AZWX AY XW a. ATSU AXVW # SSS E SAS

A: which criteria follow to congruent triangle

Q: Show that [o 2] A 3 0 has no A = L-U factorization where L is lower triangular and U is upper…

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Q: i =r+ 1+1 1le n de bifureation? on?

A: This is a problem of Dynatic Model, stability Analysis.

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: IS T Mene (R) -7 Pz(2) defined by T()= a +2bx+ (C +d )x² In lerti ble ? If so fiad its inverse thet…

A: The answer of given question is given by using some properties of inverse linear transformation.

Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: for z = In(2® + y*). Find

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

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Q: S eln (1-t) 1-t - dt ed to you in any form

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Q: Find values a, b, c, d such that the function (x+ 1)³, -2 < r <-1 s(x) = { ar³ + bæ² + cx + d, -1 <…

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Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: D.4) show that is boundled) abng the if I sinz line&CXoy):dX-By =of Straight then

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Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: Investigate the stability of the following sys (Consider the quadratic form as lyapunor system.)…

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Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: (-1+i/3)°, by using deMoivre 's theorem

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Q: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

A: Given, 2x²=1+5y² Here 5y2 is a multiple of 5 ending in digit 5 or 0. 2x2 can end in 1 or 6 But no…

Q: 2. Prove this using indirect proof in two-column form. Given: MP I NO Prove: ZNPM is not a straight…

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Q: Q[V2 ]is Principal Ideal Domain..

A: Q[√2] is Principal Ideal Domain. True.

Q: Verify by direct substitution that Un(x,y)=sinnx sinhny is a solution of Uxx+Uyy=0 for every n&gt;0.

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Q: Q:If a.ß are roots of ax +2bx +c = 0 and a + 8.ß + 8 be those of b2 - ac в— АС a Ax +2Bx + C = 0,…

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Q: + bx +c=0. If a.b.c are in HP and a,ß are the roots of ax" then prove that the HM of a.ß is (1+ aß)

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Q: e[V5]is Principal Ideal Domain. True False

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Q: B a. In the figure, if AX = (3x + 1) cm, BX = 4x - 1 cm, AY = 4x + cm, YC= 5x-1 cm and x = 2, prove…

A: SOLUTION-

Q: In AXYZ, ZY=90° and ZX=4°. ZZWY=56° and XW=820. Find the length of WY to the nearest 1oth.

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Q: 1. (a) Let 5 -6 -6 B = |-1 4 2 3 -6 -4 Find oigon nigon un imil to D

A: To finding the eigenvalues and eigenvectors to the given matrix we use Gaussian elimination method.…

Q: 3.2 Check the definiteness of the following constrained quadratics: (i) Q(x, y) = x2+ 4xy - y²,…

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Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: Consider the following quadratic form; F(x,y) = ax? +2bxy + cy. Examine under which conditions on a,…

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Q: Q[V2]is Principal Ideal Domain.. True False

A: We know that every field is principal ideal domain.

Q: Qし If xと -l Sx S2 fa)= { 5-x fo) = 2< x S3 - Is fox) Condinuons at x =2 2 and sketch this funclion

A: Hello, Thank you for the question. According to our honor code can answer only one question at a…