EX: f(x) = x* – 9x3 – 2x2 + 120x – 130 equation has a root in (1,2). Find this root with approximation error ɛy <0,0132

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: use method of False Pasition to find the Solution acurate to within lo for 25x43 and

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Q: Let v, = V2 = - 2 and w = - 1 Determine if w is in the subspace of R° generated by v, and v2. 3 - 5…

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Q: 10 -7 Let u = and v = Compute u • v, v · v, ||u|| and find the dis- 13 16 tance between u and v.

A: Given  u=10-7135 and v=-44316

Q: If / 10 - 7x2 sf(x)s/10 – x² for - 1<x<1, find lim f(x). lim f(x) = x→0

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Q: Q3. Find the solution of the given initial value problem d?x dx dr2 ++ x = 0, x(0) = 2, x(1) = 3 dt2…

A: Given that  The differential equation is  d^2x/dt^2+dx/dt+x=0 x(0)=2,x(1)=3  To find teh general…

Q: Possible values of x and y that would make the following matrix A singular, are: 4 -2 A = 2 -1 x y…

A: A matrix is said to be singular if determinant of matrix is zero. Let us find the determinant of…

Q: (Secant Method). All numerical answers should be rounded to 7-digit floating-point numbers. Given a…

A: Given: The given equation is x-sinx1-cos x=0.77 . The initial approximations are given by p0=2.6 and…

Q: Define a neighbourhood of a point. Show that the intersection of the family of all neighbourhoods of…

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Q: For each problem find square matrices which satisfy the given conditions. You don't have to justify…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: Find the solution of the given boundary value problem d²x dx 6x = 0, x(0) = 1, x'(0) = 1 dt %3D - -…

A: In this question, we solve the differential equation using initial conditions.

Q: Determine the dot products of the following pairs of vectors. (a) (2, 4), (3, -4) (b) (3, –2, 5),…

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Q: he table below gives values of f(x) = e f(x) fx) 0.94 0.95 0.96 0.97 0.98 2.55998142 0.99 2.69123447…

A: Given: Here the given is f(x)=ex. We have to compute f'(1.0) and f''(1.0) with the following data…

Q: Consider the vectors V1, V2, V3 and b. 1 2 8 -2 V1 ,V3 -13 6. 12 18 Write b as a linear combination…

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Q: Let n € N. Use the rational roots theorem to prove that √ is rational if and only if it is an…

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Q: Q5. Use Newton's interpolatory divided- difference formula to construct interpolatin polynomial of…

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Q: Identify an analytic anomaly why numerical integration formulas will fail for J_11-x² sin(ax) dx.…

A: Given integral is∫-11sinπx1-x2dx

Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: 1- Find the solution of the following second order differential equation d?y(x) dy +x- +x? y(x) = 0…

A: I assume k instant of j  If you want solution in terms of j  then you replace k by j

Q: Define the linear transformations T:R R2 and S: R R so that 3. X1 + X2 -X2 and S X2 -I - 12 a.) Is…

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Q: An ecologist examined 100 male mice and 100 female mice for signs of tick infestation. To test for…

A: The row and column total have been calculated and they are shown below:   Ticks No Ticks Total…

Q: Consider the spreading of COVID19 on an isolated South African village with population size 12 000.…

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Q: is a sequence of "nested" Show that if A, 2 A₂ 2 A3 2. nonempty sequentially compact subsets of R2,…

A: Given :  A1 ⊇ A2 ⊇ A3 ⊇ .... is a sequence of nested non empty sequentially compact subsets of ℝ2.…

Q: Find the kernel and nullity of the transformation T. T(f(t)) = f'"(t) + 4f'(t) from P, to P2 %3D

A: Let T be a linear transformation from a vector space V then according to dimension theorem ,…

Q: 5. One of the popular 3-point numerical differentiation formula is given by -3f(ro) +4f(xo +h)-…

A: This is a problem of Numerical Analysis.

Q: linear algebra

A: 6. The given matrix is

Q: Graphical re

A: Any point on the Cartesian coordinate system can be represented as: x, y. The vector: x, y is…

Q: Q5. Consider the set of all positive real numbers of the form 0.did;dida wo 2", where di 1 and dz,…

A: Solve it.

Q: Construct Newton's forward and Backward Difference polynomials to approximate the following function…

A: To obtain the interpolating polynomials, use the following formulae. Newton's forward difference…

Q: State and Prove the diggonally dominent Condibion af convergence of Guass-Jacobi and Gauss - Siedel…

A: We have to solve the given question from numerical analysis.

Q: et f: [a, b] → R be a function, where a and b are real numbers with a < b. (a) Prove that if f is…

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Q: 9. Write the complete solution x = x, +x¼ to the given linear system. x + 3y + 3z = 1 2x + 7y + 9z =…

A: Given : Given system of linear equation is x+3y+3z=12x+7y+9z=5-x-3y-3z=-1 We want to write complete…

Q: Q4. Find the eigenvalues and associated eigenvectors for the given matrices. -2 -4 2 B = (-2 1 2 4…

A: Eigenvalue is calculated using characteristic polynomial. Characteristic polynomial  is given by…

Q: 1) Using the bisection method and the interval [-0.3,1.7] ,to get an absolute error less than ɛ=0.04…

A: The root of the function can  be calculated using the bisection method. The method approximate the…

Q: I. II. Given f(x) = 1/Inx' approximate f(x) dx the Trapezoidal Rule with four subdivisions to 3…

A: Let       take   and number of sub intervals n = 6 then…

Q: Define a function called approximate_newton (f, h, x0, epsilon, maximum iterations), where f is the…

A: As per the question we will construct a Python code that implements an approximate version of…

Q: 4. Use Cramer's Rule to find x for the linear system given by x+ 2y – z = -1 3x – y + z = -6 2x - 2z…

A: The given linear system is                                          x+2y-z=-13x-y+z=-62x     -2z=-6…

Q: (3) (a) Let T be a surjective linear transformation from P7 W. Show that dim(W) dim(W). Lastly, the…

A: Given below the detailed solution

Q: f(x) = +- 3.437 %3D Find (for your own use) the derivative f' (2) of the function f(2). (i) We claim…

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Q: 04: The linear system of equations 2 10 X 4 1 1 0| x, | = 0 0 2 || X3 2 has an exact solution i =…

A: Given: The linear system of equations: 210110002x1x2x3=43-2 Exact solution: x=12-1t

Q: Q1: Use a Lagrange method to find f(1.3) and f'(4) for the function f(x) given by the following…

A: To find f(1.3) and f'(4) using the Lagrange method.