Use the Newton-Raphson iterative to find the root of the function f(x) = 2 Sin (X)-X²+1 in the interval [-1,0], to an accuracy of three decimal places.

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Q: 2. Let R be an integral domain (a) Define prime element and irreducible element (b) Prove every…

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Q: O Compute the Transitive Closure of the following relations on the set A={1,2,3,4}. (i) R₁ = {(1,2),…

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Q: 11, 31. Find the flux of F = (x²y, xy, y²z³) across the cube bounded by the planes x = y = ±1, z =…

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Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

A: Given : A volume is given by the iterated integral  ∫y=-1y=1∫x=y2x=1∫z=0z=1-xdzdxdy To Find :Plot…

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Q: for Suppose the vector field v(x, y, z) = 3zi+ (2x − 3) j+ 4x k represents the velocity field of a…

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Q: limit as x → 1 of In x x-1

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Q: Find the critical points, domain endpoints, and local extreme values for the function. y=…

A: Let,  y=f(x)=-x2-4x+5,  x≤1-x2+5x-4,   x>1. Clearly, f(x) is defined for all x∈ℝ.  Hence, domain…

Q: The function I (t) = - 0.2t3 + 3t2 +100  for 0 ≤ t ≤ 9 gives the CPI of an economy, where t = 0…

A: It=-0.2t3+3t2+100 for 0≤t≤9

Q: 7. Draw a pair of lines I and m such that polygon ABCDE is rotated to polygon A'B'C'D'E'. Note: This…

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Q: Estimate the area under the graph of the function f(2)=√√2+5 from z=-3 to z = 4 using a Riemann sum…

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Q: Suppose the class equation of a group G is |G| = 1 + 4 + 5 + 5 + 5. Show that G has an element of…

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Q: = 17. Evaluate fF.dr, where F(x, y) centered at the origin. -Y x 2,7²²), and C is the circle of…

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Q: 3) d²x cl+²2 Now + 8clx dt (D² + 80 +25)X = 10 ult) u(t)=0 when, + 20 2 (0² + 80 +25) x = 0…

A: For first part, We know that series of (1+x)-1 = 1 + x + x2 + ... Using this we expand where x =…

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Q: why does z go from x2+y2 to 1?

A: Sketch the region E.

Q: If a, b, c are in A.P., then prove that the following A.P. (i) a²(b + c), b²(c + a), c²(a + b) 1

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Q: if sisa group of order p", then its center 2 pleing a prime s

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Q: Determine convergence or divergence of the series using ratio or root test. Clearly identify the…

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Q: The general solution of the DE (x² + y² + 1)dx + x(x − 2y)dy = 0 is a) x² + y² + xy + 1 = Cx O (a).…

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Q: 4. x and y are two positive integers. (x,y) = 5, Icm (x,y) = 200 and 15, find x and y. gcd x - y =

A: Given that     gcd(x,y) = 5 ;   lcm(x,y) = 200   and  x-y = 15 Formula :     xy =…

Q: 5) Using transformation and integration, find the area of the region that is enclosed by the ellipse…

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Q: Corollary 4.3. Let 2 and m pairwise co-prime and m = mmm. m} be positive integers such that they are…

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Q: (b) y = (x + 1)e™* y+y-e* = 0

A: To verify that the given equation is a solution of the given differential equations

Q: Consider the system of differential equations xi(t) = 3x₁ (t) + 2x2(t) x₂ (t) = x1(t) + x₂(t) + e²t…

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Q: 1.) dx dt +7x25 cos 2t ← Equation 1

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Q: Consider group G and its subgroup H (H ≤ G): [G : H] = 2. Prove why H is a normal subgroup of G.

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Q: 3. Let V = R[x]4 (polynomials of degree at most 4). Let T: V → V be the linear map given by T(ƒ) =…

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Q: Evaluate the following summations. (e) Σ2000 (2+3k). k=0 200 (f) Σ% 2 · (1.01).

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Q: Prove each of the following statements using mathematical induction. (d) Prove that for any positive…

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Q: If V is a vectorial space over R with inner product. Show that u Iv u,νεν, λε |||u + 2.v|| ≥ ||u||

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Q: b) Give an example of a function g: R →R that is continuous at some xE R, but not differentiable at…

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Q: 3. y" - 2y' = ex (x² + 2) cos2x 4. y" - 2y' - 3y = 4x - 5+ 3xe ²x

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Q: 2x4-3y4 lim (x,y) (0,0) x4 +y4 b) x³y³-1 lim (x,y)-(1,1) xy-1

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