Fill out the blanks: 1/ 1+ Han²x = ( Pythagorean identity) 2/ Express Sin 2 x in terms of sine & cosine. 3/ Half-angle formula for sine : Sin &/2 = Sin I = 4) Sin =

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Q: How can I prove "A graph is k-colourable if and only if it is k-partite.”?

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Q: 2. Consider the iterated triple integral 2₂ (b) Sx²+²xz dz dx dy in Cartesian Coordinates. Sketch…

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A: Question 6 is to determine the significant zeroes.

Q: Find a QR factorization of the matrix A. 8 12] A -4-36 0 12

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Q: Find the specified change-of-coordinates matrix. 7) Let B and C be bases for R²2, where Find the…

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Q: The actual table is given -1 2 – α 0 1 1 -1 2 For those values of a for which the matrix A is not…

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Q: many black balls are need

A: The correct answer is: 200      N.B: For nth term, we need 2n black balls.

Q: Evaluate the following integral COS Z $, 2 (205 215 2dz, one each of the following closed curves y:…

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Q: Find an LU factorization of the matrix A. 3 5) A = 6 24 7 3 6 -5 22

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Q: Given the graph of g(x), select each x-value for which g'(x) > 0 (the derivative is positive). y W…

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Q: S x³dx - T ≤ 0.005.

A: To find: The value of N. To use: Error bound for TN. Given: ∫01x3dx-TN≤0.005

Q: [A] 2 5 8 and [B]= 2 5 8 2. Multiply the matrices as follows d. [A]¹[B] (C)=4 and (D)=5

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Q: The actual table is given 12 -1 0 2 -α 0 0 0 1 Find the values of parameter a for which matrix A is…

A: A matrix A is contested if det(A)≠0 We have to find those values of α for which det(A)≠0.

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Q: Classify and sketch the graph of the surface 25x^2+y^2-z^2-6y+6z=0 (show the vertex)

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Q: -1 d) p(x)=√√4x³-7 e) g(x)=x42³x-1 f) p(0) = sin² (40)

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Q: 1. X (y) = -1 X 2)() 8 4 12 V

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Q: .1/3 Let f(x) = x¹/3, and let T₁(x) be the nth Taylor polynomial of fcentered at a =

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Q: 2) Describe all solutions of Ax=b, Describe the general solution in parametric vector form. 2-5 3…

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Q: et 8- ((1, 2), (-1,-1)) and 8- ((-4, 1), (0, 2)) be bases for R², and let A-83] А we the matrix for…

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Q: [1² dy dx = rdr de rde dr+ √2 rde dr

A: Let x-1=rcosθand y=rsinθ.Now given 1≤x≤2 and 0≤y≤2x-x2.So y=2x-x2⇒x2-2x+y2=0…

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Q: The function f(x) has been transformed to y = -2f(-x+3)+1, which has resulted in the mapping of (4,…

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Q: Simpsons & mule : Śh f(x dx a h = b-a, 2 J-8 S₁ √₁+x³ dx = b f(x) dx = 1/2 [ Yo + y₂ + yon 3 1 (8₁…

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Q: Problems In each of Problems 1 through 11: a. Seek power series solutions of the given differential…

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Q: Given the points X(1, 2, -1), Y(0, 3, -2), and Z(-2,6,0), find ZX in AXYZ.

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Q: Find the general solution of the differential equation d²y dy dx² - 5 dx +6y=e* + e²x.

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Q: Consider the curve C defined by (x; y) = r(t), where r(t) = (t; (1+t)/t; (1-t^2)/t) ; t > 0: (a)…

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Q: Solve the initial value problem y = 8 +32x+160x² + 800 3 y" + 5xy' — 20y = 0, y(0) = 8, y'(0) = 0. -

A: The given initial value problem y''+5xy'-20y=0, y0=8, y'0=0. We have to find a solution to the IVP.

Q: In each of Problems 17 through 19, find the Laplace transform Y(s) = L{y} of the solution of the…

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Q: Find a singular value decomposition of the matrix A. 18) A= -1 2 1]

A: Singular value decomposition: The Singular value decomposition of a matrix is a factorization of the…