Q1) Determine the missing value's in the table. the forward divided differences are given by X y(x) 1st order divided 2nd order divided --- -0.1755 0.4381 1.1 2 3.5 --- 2.1287

Q: 1 (-1)-1 (ii) 1 +... 5 2n-1 (b) Show that the interval of convergence of the series 1 1 -√2ses.…

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Q: t(M₂ (R), +..) be a ring. Prove H = {(8) a, b, c E R}is a subring of 10 ), +..).

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Q: Q2) Let(M₂ (R), +,.) be a ring. Prove H = {(a) la, b, c € R}is a subring of (M₂ (R), +..).

A: A subset H of a ring R is a subring if: ∀a,b∈H we have a-b∈H ∀a,b∈H we have a.b∈H Now, we have…

Q: Ju udv-uv- 1 [vdu to Explain why the substitutions below are inappropriate. Let dv <=x x dx 1.…

A: Here we will find how to use integration by parts

Q: Q2) Let(M₂ (R), +..) be a ring. Prove H = {(a) la, b, c = R}is a subring of (M₂ (R), +,.).

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Q: (c) Let D be a square with sides 0≤x≤ 2 and 0 ≤ y ≤ 2. Estimate the following integral ff (x + 1)"…

A: Solution: Given integral ∬Dx+1ydxdy , 0≤x≤2 &amp; 0≤y≤2 Now, ∬Dx+1ydxdy=∫02∫02x+1ydxdy

Q: Question 5 ( T A manufacturer assembles personal computers. If the computers are priced at £1,000…

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Q: 4. Prove that a permutation matrix is orthogonal.

A: Permutation matrix: Each column of a permutation matrix has only entry equal to 1 and all other…

Q: 4. ABP is a triangle, M is a point on AP. AB = a, AM = 26, and MP = b. N is the midpoint of BP. C is…

A: Follow the steps.

Q: EX. 26 Let G be a group in which x² = e for all x € G. 1. Show that G is abelian. 2. Deduce that…

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Q: Assume that f(x) is a function defined by x²-3x+1 f(x) = 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x) is…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Determine the nature and stability of the equilibrium points of the system dx = x = y + x², dt dy…

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Q: (a) Let f: R" → R be a function given by f(x₁, 2,...,xn) = x²₁₁x²2x², where n = 1. Show that the…

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Q: 2. Let the function Prepresent the population in billions of a country P (t) and represented by the…

A: Since  you have posted a multiple  question according to guildlines I will solve first  (Q2)…

Q: 9. Suppose only the top 20 % of marks on a university entrance exam qualifies an application for…

A: Here we can use normal distribution to find the minimum marks to be in top 20%. If x are minimum…

Q: Verify Stokes' Theorem for F(x, y, z) = (y,-x, yz) and Sis 13.) the paraboloid z = x² + y², 0≤z≤1.…

A: Let S be a open surface bounded by a closed curve C and F=f1i^+f2j^+f3k^ be a continuous…

Q: Obtain the general solution to the equation. (x² +19) dy dx + xy - 2x = 0 The general solution is…

A: Using integrating factor method

Q: 7 Angles x and y are located in the second quadrant such that sinx= a) Use a right angle triangle to…

A: a) and b)

Q: Q4) Evaluate the integral 0.5 0 N=6. x sin(x) . dx using trapezoidal rule taking

A: We need to find the value of integral ∫00.5xsin(x) dx using trapezoidal rule. f(x)=xsin(x) then step…

Q: Consider the system ry, 4-4x - 2y. 1. Determine the nullclines of the system and sketch the…

A: As per the question we are given a 2d nonlinear dynamic system. And we have to : Find the…

Q: Find the quotient of B/A. Use pivotal method in solving for ALL (3x3, 2x2, ...) determinants. 3 1 3…

A: given, A=3137077468328491, B=45675678678978910 B/A=BA-1A-1=1Aadj(A)let adj(A)= C for get the…

Q: z² (3+j5)z + j8-5=0

A: We have z2-3+j5z+j8-5=0' The solution of the quadratic equation az2+bz+c=0 is z=-b±b2-4ac2a Now, we…

Q: Find the area of R = {(x,y) = R² : x € [-1,2], y € [x²,x + 2]} integrating first along horizontal…

A: The double integration in the horizontal direction is ∫ab∫g(y)h(y)f(x,y)dxdy The double integration…

Q: Find the area bounded by the given curves. 1) y = x³, y = 8, x = 0

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: 3. Let (G, *) be a group of order p, q, where p, q are primes and p < q. Prove that (a). G has only…

A: The given question is related with abstract algebra. Given that G, * is a group of order pq, where…

Q: 3. In fitting a parabola, the formula to find the sum of the squares of the residuals is a) E= Ey-…

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Q: ]x" (t) + x (t) = 6 sin 2t "here X(0) = 3 x' (0) = 1

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Q: Question 2: Determine the nature and stability of the equilibrium points of the system dz = z-y+z²,…

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Q: Question One (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x1 for 2 ≤ x ≤ 3. 1 Prove…

A: Solution : a) f(x)=x2-3x+12x-1 2≤x≤3 f(x) is a rational function and bounded because its pole x=12…

Q: მს For the function (x, y) = √√x²y², we have that 8 (0,0) = 0 and (0,0) = 0. From this, it follows…

A: As per the question we are given an argument about the first order linear approximation of the…

Q: e. S √ x e √x d x 0

A: The given integral is ∫0∞x4e-xdx To find: the given integration.

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dy y +…

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Q: LP Model Minimize: subject to: z = x-y 4x-3y ≤0 x+y ≤ 10 x.y 20

A: We have given a LP model ,  min z = x - ysubject to,         4x - 3y ≤ 0         x + y ≤ 10…

Q: Solve the equation using Variation of Parameters (D² + 1) y = tan x

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Q: If the coordinates of a triangle are given, then, its area may be solved using the formula 1 |X1 Y₁…

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Q: 2. The value of ¹₁ KIN [Tn (x)]² √1-x² 5 LEIN dx = ..., for each Chebyshev polynomial Tn(x), n ≥ 0.…

A: The given integral is                                    ∫-11Tn(x)21-x2dx where Tn(x) , n≥0, are…

Q: 5. Given that f(x)= |x|, h(x)=-x, g(x)=(x-2)²-3 . (a) Graph f(x),h(x) and g(x). (b) Using the…

A: f(x)=x, h(x)=-x, g(x)=(x-2)2-3

Q: Suppose the population of a particular endangered bird changes on a yearly basis as a discrete…

A: As per the question we are given a chicken population model in terms of discrete dynamic system. And…

Q: Suppose G(r) is the generating function of a sequence (an), satisfying G'(r)=rG(r), G(0) = 1. iii.…

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Q: 1. The LP problem has an unbounded feasible region A. True B.False 2. How many corner points are…

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Q: Derive all the possible equations of x. Given: (x-2)^2-lnx=0

A: x-22-lnx=0

Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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Q: Question Five (a) Let f: RR be a function given by f(₁,2,...) = ...., where P Σ-1. Show that the…

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Q: (a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + +. + n! 2n…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Question 5 Let the function g: R → R be given by: g(x) = (x-1)³ +5. (a) Compute g(6). (b) Show that…

A: As per our guidelines we are 3 sub parts answer only ( if there are multiple sub parts asked). so…

Q: 6. Find a basis of the null space of each of the differential operators below, and verify that the…

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Q: (b) Show that the interval of convergence of the series -1/2 sest √2 2n-1x2n-1 (4n - 3)² is given by…

A: The radius of convergence of a strength collection is the radius of the best disc on the…

Q: Find the area of this composite shape. 11 cm 16 cm 4 cm 5 cm 4 cm 4 cm 7 cm 3 cm

A: Let us consider a  rectangle with length L and breadth B then the area of rectangle is  Area of…

Q: Determine the nature and stability of the equilibrium points of the system dr = x=y+z², dt dy 12r -…

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Q: . Given: z= 6(cos30° + isin30°), find 1. 25

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