dx 4) Using the Residue Theorem, show that S (x²+4)³² " ㅍ 16

Q: エ+1 dx (7² +2x)

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Q: aud a 0: Let has no real Zeros. Find necessary and Safficient af P and a are Polynomials and Cond…

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Q: 50 50 51 7. + 40 39 40 • () - €) (") - () () - () () 7 8. 4 10 9. 2 10 8 8. 8 8. 10. + 2 3 6.

A: We can solve the given problem using concept of fractions.

Q: 7x-2 b) xp: 3x-1

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Q: b) I =f- x(1+(In x))

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Q: y² + y²e6)° x' 2 + 2x²eG)* , 2xye 2xye 6)*

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Q: If y = (1+x)8 (x + 1)7 True False then dy dr

A: We can solve this as follows:

Q: Evaluate the expression (In (3.34)- tan (61.010)-2)/(5.011e0.37 +1)

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Ex:. Find the fourth roots of Z=-di Say no 4 K = 0₁12₂3

A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: (g) 2s²+3 (s + 1)²(s² + 1)²

A: Fs = 2s2+3s+12s2+12                                                     1Fs =…

Q: (b) Find a closed-form expression for Ak+1, k1, where 0 0 23 30 -18 -235 A 0 9

A: Given that Now the eigenvalues of A obtained from Eigenvector corresponding to .

Q: For &) r 0x xi روا show that ܕܕܥ in the region where #0

A: Given that .We need to show that (a) , and (b)  in the region, where  in .We know that .

Q: -4 6. |a + 3|dx – 1)³ydy -1

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Q: 28 If √1− xº + √1− yº = a³(x³ - y³) lf dy 1-y6 2 x²

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Q: Q₂i- If show that utt ч (хо) ut (x,0) - a 9/x). Z 3 u (X, Z) 2 Ux(xt) = a as 1x1_-2 ux 9. 2 u XX…

A: Using D'Alembert solution for one dimensional wave equation.

Q: 6n2 + 3n = 3 2n2 – 5 Prove: lim

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Q: A6. Using Taylor's expansion, expand the polynomial f(r) = 2r - 13r + 28r - 11 in the form f(r) = ao…

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Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

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Q: 7. lim /* √x² + 8 dz h→0

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Q: Part (b) 5e Evaluate -dz by residue theorem, where C is the contour |z| = 2 6z4 +30z3

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Q: A particle is moving along the path given by: x = t2 , y = t³ over the interval 0<t<1 Calculate the…

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Q: ising residue theorem prove dr x+1 2

A: Given:

Q: Prove from the definition: n3 + 65n2 + √n = Θ(n3)

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Q: Evaluate the improper intergal 1 dxusing the residue theorem. (x2 + 9)?

A:

Q: x- 1 lim Vx² +3 – 2

A: given limit

Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

A: Given function is  Fx=∫1xsin2tdt

Q: If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the…

A: Let the given integral is  --------- (1)            For evaluate the above integral consider the…

Q: (c) (z-a)", where a EC and n = N*

A:

Q: Q5) Find the root of f(x)= 5 sin(x) + ex² by using bisection method take a= -1.25 and b= -1.0 for…

A: Given, fx=5sinx+ex2. Here, a=-1.25b=-1.0 Now,…

Q: DeMorgan's theorem states that Select one: a. (A + B)' = A' * B b. (AB)' = A' + B' c. A' + B' = A'B'…

A: We are given some statements to verify De Morgan's theorem. We can do this in the following way:

Q: Yn+1 = ayn-p+YYn-h (yn-h) 9-¹+8 +6

A: Given: The information showing the proof of a specific theorem.To prove: yn+1=αyn-p+γyn-hyn-hq-1+δ…

Q: CoS X F 2x 7x

A: