Q4) Choose the correct answer: 1- Bessel function is a) odd function b) even function c) odd & even d) none of these 2- The value of S V-2 (x) – J2(x)]dx is equal to a)0 b) -2 c) 2 d) 1 3- If Jn+1(x) = In(x) – Jo(x) then n is a)0 b) 2 c) -1 d) none of these

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A: The cubic spline is defined as: Sx=S0x=1+2x-x3 if 0≤x≤1S1x=a+bx-1+cx-12+dx-13 if 1≤x≤2 From…

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Q: 2. Using OLS or any other suitable method, Prove that E(ß1) = B1 E(ßo) = Bo

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

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Q: 4.Determine the correct Wronskian setup for v, and v, for the equation y" – 3y + 2y = 10sin(x) e 2x…

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Q: (a) Define the symbols ôf/DE and af/dz by af 1 (af 10f 2 (dr af 1 (of 18f i by, dz 2 dr' i dy as…

A: Since you have asked multiple questions, we will solve the Question (a) for you. If you want any…

Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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

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A: This is a question of the Theory of Reimann Integration.

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Q: 4. a) Prove that i) V=1 ¡¡) fx+nh = Σk=0 I A I+A 1+A (1) Ak fx.

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Q: prove that F(r) = 4z-3z is chaotic on the interval [-1,1]. (Hint: consider g(6) = 30 on S'.)

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Q: 6. Consider the ODE system below f = y? - ,2 = y +?. Which of the following is true? a. Solvable by…

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

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

A: Demoivre's Theorem

Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint & z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

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Q: Q/Use Definitien 13.4-1 +o prove that f(x,r}>x+y' is difterentialeat (o,0).

A: Given function is  fx,y=x2+y2

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Q: In Exercise 5.8, we derived the fact that 4y1 Y2. 0< yı < 1,0 < y2 < 1, f(y1. y2) = 0. elsewhere.…

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Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

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: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

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Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

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Q: (c) Evaluate d Gosh: where C: |z| = 2 by using Cauchy's residue theorem.

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Q: Defn `x→- `xj diverges to minus infinity" VR>O 3N, such that Vj zN *j<-R 8;<- R Hw7 het x; = - 8j…

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Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: that X and Y have joint pdf f(x, y) ={x + 3x^2y if 0 <= x <= 1 and 0 <= y <= 1, 0 otherwise.   (c)…

A: From the given information, Consider, the Joint pdf of X and Y is as follows: fx,y={x+3x2y if…

Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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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…