What is the power series for ln(2-x^2)

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Q: 7. Show that the characteristic of an integral domain D is either 0 or a prime p.

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Q: Consider the following equations. • Res(f(z), Zo) = _lim (z-zo)f(z) Z-10 1 Res(fiz), z)= • Res(f(z),…

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Q: Find Taylor series of the function f(x)=4-9about = 0, and determine its interval of convergence.

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Q: EVALUATE: A = [² [²√² + ¹ dydr 1 X HINT: Perform a reversal of integration

A: We have plotted the region of integration in the following figure(shaded in yellow).

Q: Evaluate by the residue theorem: So (1+x²)(4+1²) [12).

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Q: 3. Use the Taylor polynomial around 0 of degree 3 to the function f(x) = sinx to find an…

A: fx=sinx

Q: Find a basis for the null space of the matrix. Show All Your Steps. 2) [10-7-2] A = 01 7-2 100 0 0

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Q: Find the solutions x*(r, s) and y* (r, s) of the problem max f(x, y, r, s) = max(r²x + 3s²y = x² –…

A: max fx , y , r,s=maxr2x+3s2y-x2-8y2 To Find: x*r , s , y*r , s

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Q: [10] (4) EVALUATE: 2 e 1 A = - = √°S ² √ y ³² + 1 Inx X dydr HINT: Perform a reversal of integration

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Q: ● Solution : Question 6: If A = b C def h a 9 det (3B-¹) when B = 2 " with det (A) [5g 2a -d] 5h 2b…

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Q: A matrix A is given along with an iterate x5. - [ A = - 3.5 2.5 2.0 3.0 813.500 (a) Use these data…

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Q: [10] (5) GIVEN: a > 0, -a ≤ x ≤ a - (4x) +505 = (x, y) 0 ≤ y ≤ R √a²-x² 2 2 EVALUATE: A = √√√x² + y²…

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Q: 2. List all elements of A = M₂ (Z₂). Give the units in A, as well as the zero divisors in A.

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Q: Find • S/ 1₁2 ª z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), and…

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Q: Chapter 5 Question 11: Determine whether the given two matrices are similar : Г0 -1 A 1 2 0 and B= 2…

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Q: Problem 7.5: Using any one method to find the GS of X' (t) = [²4] x (t) + [³²] 15

A: According to the given problem, find the general solution.

Q: 9. Let F be a field of characteristic 2 with at least 2 elements. Then for some x,y in F (x+y)³ ‡ x³…

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Q: The graph of f is shown. (b) (c) 1620 FK. 40 y 14 › [th* 120 4 0 f(x) dx Evaluate each integral by…

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Q: Prove W.O.P.M.I., i.e. prove W.O.P.M.I. and prove M.I. ⇒ W.O.P¹8

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Q: Find the eigenvalues of the given matrix. -24 25 -20 21

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Q: 2) Consider the following table; The polynomial x 0 1 2 3 4 56 1 -1 3 P3(x) = 1 − 2x + 3x(x − 1) —…

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Q: Find the area of the region. 2ex 1 + e²x y = -2 -1 y H₂ 3 x=ln √3 + X

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Q: 30 + 23s + ܐܨ7 (s − 2)(s² + 25 + 5) –

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Q: Let p be an odd prime and a be a quadratic residue of p. Prove that if p = ±1 (mod 8), then 2a is…

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Q: 13. Suppose that a and b belong to a commutative ring and ab is a zero divisor. Show that either a…

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Q: Use the Laplace Transform method to solve the DE: initial conditions y(0)=4;y'(0)=0 y"+y=√2 cos(√2t)…

A: Given differential equation y"+y= √2 cos(√2t)  Initial conditions y(0) = 4, y'(0) = 0

Q: 5. Find the plaintext message if the ciphertext produced by exponential encryption (§8.3) with key…

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