Given the function f (x) = x3 + x - 1 = 0, a) Show that the equation has a root in the interval [0,1] 2xn3+1 3xn²+1 b) Use the Newton-Rapson formula to show that xm41 = c) Hence, find the root to 2 d.p.

Q: 1. /v + x = z, for v Solve

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Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Find all solutions on interval [0, 27): sin(30 + ) = 1. 6.

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Q: Find the roots of function f(x) = x 3 − 2x 2 + 0.25x + 0.75

A: It is required to find root of x3-2x2+0.25x+0.75=0. Now, 13-2×12+0.25×1+0.75=0. Thus, x=1 is a…

Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: Solve for r: 3x2 = 4x - 2. 2 + 2/2i (a) 2 + 2/10 (b) 3 3 (c) 3 2士 0 (d) 3 (e) None of these

A: Given,              3x² = 4x - 2

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Q: Calculate the first three approximations x1, x2, x3 to a root of f (x) = x2 − 5 using the initial…

A: fx=x2-5,   x0=2 Differentiating with respect to x, we get f'x=2x Now,…

Q: Consider the function y=x6−2. Do the following steps: 1) Find the tangent line at x=1 2) Find the…

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Q: Find the exact values of x in the interval [0, 3pie] that satisfy the equation sinx= -1/2

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Q: ne x1 and x2 for the fu

A: In numerical analysis, Newton's method, also known as the Newton–Raphson method,  is a root-finding…

Q: esz+1 dz, where C:|z- 5|= 1, counterclockwise, is z - 25 The value of

A: We have to evaluate the integral ∮ e3z+1z2-25dz over the circle z-5=1. We have to find the points…

Q: 2. Find an estimate of the root of the equation: 2* + Vx² +5 =20 using regula-falsi method. Ans

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Q: 5-3x S2 4 Solve (1) ans./ [-1, co)

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Q: Which of the following most nearly gives the value of the real root of f(x) = 5x³ – 5x² + 6x – 2…

A: Given function is fx=5x3-5x2+6x-2 initial guess :- xl=0  and   xu=1

Q: Find a value for x so that distance from (x,3,6) to the origin is 9

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Q: Solve the equation (2cos x - √3)(2 sin x - 1) = 0 on the interval [0, 2π).

A: To solve the equation 2cosx-32sinx-1=0 on the interval 0,2π. Solving the given equation.…

Q: Find the root/s using the regula-falsi method. PLEASE COMPLETE SOLUTION until f(root) must be equal…

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Q: w = (1³ + 11)8| dw dt

A: Given :   To find

Q: 9. Find all roots of f (x) = 2x° + xª – 5x³ + 10x² – 52x + 24 given that 2i is a root. %3D

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.