Use the residue theorem to prove that: dx x√x² - 1 || Π - 2 1

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: 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: Q2 Let C = {r : x e Z}. (a) Show that C'nQ+ 0. (le. show C contains a rational.) (b) Prove that…

A: We know that Tr = set of all transcendental number is conutable  And any subset of conutable set is…

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

A: If Q5 is a field, then it will be principle ideal domain. It suffices to show that every element of…

Q: Solve for the Maclaurin series expansion of ex and use the series to evaluate e0.3 which must be…

A: Maclaurin series

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: Q5 (i) Prove that the chromatic polynomial of K2_s is (ii) Prove that the chromatic polynomial of Cn…

A: Solutions

Q: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

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Q: 20xth)t xth 3. Zx- Find the limi,t

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Q: し- [x. +J+aCy-XP.-sPz> what is the paihial of x, ? derivahire in teams

A: In partial differentiation, we find the rate of change of a function with respect to one variable…

Q: Let f and g be the functions defined by f : R → R+ ∪ {0} with f (x) = x2 and g : R+ ∪ {0} → R with…

A: (fog)(x) is the value of the function f(x) at g(x) (fog)(x)= f(g(x))

Q: 6n2 + 3n = 3 2n2 – 5 Prove: lim

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Q: Show that: 8 [J₁(bt) t" eat dt ed 0 2"b" I(n+-) 2 n+- 2 √√π (a² + b²) T

A: To prove the given integral identity, we will use the integral representation of the Bessel function…

Q: Evaluate the following complex functions and show your complete solution

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Q: Use the basic definition (Ad-hoc Calculations) to show that f(x) = x4 + 2x3 − 7x2 + 3x − 6 ∈ Θ(x4)…

A: Using the limit definition of big O and sigma definition we can prove this thing.

Q: 3. Determine the pole and the residue of 22+1 f(x) 24-z-2

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Q: Prove that √2+1 = 2√√(2) using √z = t²-1 et dt

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Q: 2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If d(x) = gcd(f(x),…

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Q: x+3 Evaluate: S dx 5-4x-x A. -V5 – 4x – x² + arcsin+ C x+2 B. -V5 – 4x – x² +arcsec+C 3 C. -V5 - 4x…

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Q: The real part of sech (2-j3) is -3.7245 -3.5906 O 0.0403 O -0.0106 -0.5309 1.0357

A: The Euler's formula is widely used formula in complex analysis. It makes a bridge between the…

Q: Suppose that Pr[A|B]=4/7, Pr[B|A]=8/13, and Pr[A′]=8/21. Find Pr[A∩B′].

A: To calculate the required probability (using the data on conditional probability)

Q: 2a In R^ show that : 2 as 211x11² + 211|4|1²³ = || Xx+y|11² + 11x-y₁1² ( This is known a the…

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Q: Show that 1 + 3x is a unit in Z9[x].

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Q: 2 ez Let f(z) Let c be the (z - 7)(z - 9) circle |z| = 11 in the counter-clockwise %3D direction.…

A: It is given that the complex function fz=2ezz-7z-9. We have to evaluate the integral ∮C fzdz, where…

Q: lim t→l 1+√t+ √t+√t t² + 1 + 1 t³-2

A: I have solved step by step in detail...and I have written answer up to simplified…