Evaluate the following integral using Cauchy's Residue Theorem. 2+3 $ √√2-51=3 (z − 3)(z - 6)(z- 9) dz.

Q: 3. For the function g(x) = x³ – 2x? – 11x + 12, use long division to determine whether each of the…

A: we devide the polynomial by given factor and if we get remainder zero then this given factor is…

Q: press the improper rational transform: 3 4 X(z) = 1+ + + 1 3 ms of a polynomial and a proper…

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Q: 10. Let h be the function defined by h(x) = x* – 8x3 + 23x2 – 28x + 12. Use the Rational Root…

A: To write the possible rational roots

Q: Evaluate 3z2 + 4x + 2 is negative. 3z? + 4z + 2 is an irreducible quadratic since the value of b² –…

A: Given

Q: Let a E K and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is ƒ(a).…

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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: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

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Q: a(bx+j)(cx+k)(dx+m)² (ex+n)(gx-p)(hx+q)' with the following conditions a,b,c,d,e,g h.j,k,m,n,p.q are…

A: Given type of function is fx =abx+jcx+kdx+m2ex+ngx-phx+q

Q: Use the Residue Theorem to show that sin²x ㅠ f² = 0 x2 dx = FIN 2

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Q: Find √ √ [V³ [V** ry sin(x² + y²) dzdy

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Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Stan and Ollie work on the integral J2x(a* + 2) di. Stan lets u = x? + 2 and proceeds to get (x + 2)…

A: Since, we have been given that Stan and Olie work on the integral:-∫2x(x2+2) dxIntegrating the above…

Q: 6. Simplify the rational expressions (a) st = ut 24 w %3D (zw)

A: As per bartleby guidelines for more than one question asked only first is to be answered please…

Q: Use the residue theorem to evaluate: o dx 0 x3+1 2n/3

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

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Q: The PG(2, q) has 133 points. Find algebraically the value of q in PG(2, q). Note that q is the…

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Q: Find the roots using Bairstow's method of the function f (x) = x* – 2x3 + 2x² + 3x – 4. Use u, = 1…

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Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: 6/30° + j5 – 3 (а) -1+j+2ej45° (15 – j7)(3+ j2)* (b) - (4 + j6)*(3/70°) means you need to conjugate…

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Q: Find the rational roots of x* + 8x + 7x-40x- 60= 0. 02,6 О-6, -2 O-2, 6 О-6, 2

A: Given  x4+8x3+7x2-40x-60=0 let, f(x)=x4+8x3+7x2-40x-60 Given that there is at least one and possibly…

Q: The zeros of the polynomial function f(x)=x² – 2x² – 15x are: a. {-5,–3,0} . b. {-3,5} . c. {-5,3} .…

A: We have the given function as fx=x3-2x2-15x On solving further by making factors, we get the result…

Q: Taylor's

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Q: multiple of a and c: =b/(n^3) c = b/(1 + n^2) S 1 du au²+bu+c

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Q: x²2x+2-5n/x) Sin/2 Sesier. Find the Taylor Centered at 9=1 (x)

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Q: (c) Show that V3 e Q[ V6]

A: We have to proceed using contradiction method.

Q: Evaluate the improper intergal 1 drusing the residue theorem. (x² + 16)?

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

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Q: What are the rational roots of f(d) = 5d³ – 6d² +d – 8? Oz = -,2 = -,1 O This polynomial has no…

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Q: 4. Consider the polynomial f(x) = x* + 1. (a) product of two irreducible quadratics. Explain why ƒ…

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Q: a.) Calculate L6 for f(x)= (squareroot (9x+1)) over [1,3] Give answer to three decimal places L6=…

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Q: press the improper rational transform: 3 X(z) + 1 + z 8 ms of a polynomial and a proper function N

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Q: 5.00 Use the residue theorem to show that x² 1+x5 dx = π/5 sin(27/5)

A: As per the question we are given an improper integral and we have to show that its value is equal to…

Q: For the given function, a) list all possible rational zeros, b) factor f(x), c) find all rational…

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