The root of the equation f (x) = 0 is found by using the Newton's method. The initial estimate of the root is xe 3,f (3) 3. The angle between the tangent to the function f (x) at x 3 and the positive x-axis is 57 The next estimate of the root, x, is most nearly O 0.4024 O 1.0518 O 6.2470 O -0.24704

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A: Image is attached with detailed solution.

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

Q: Consider the following root equation. (DS/DS! 10 040 0X0 9 ƒ(x) = x³ cos () + 6 sin(x) CONS 1OXO OHO…

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Q: The root of the equation f (x) = 0 is found by using the Newton's method. The initial estimate of…

A: Given that roots of the equation   f(0)=0   is found by using the Newton's method.…

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Q: If Newton's method is used on f(x) = x³ – 2 starting with ro = 1, what is x2? What is the absolute…

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A: To find 11sinx+7cosx in terms of sine function only.

Q: 3. Find a positive root of cosx - xex = 0 upto four decimal places, using Newton-Raphson mehtod. %3D

A: I am attaching image so that you understand each and every step.

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A: Here given equation isLetand

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Q: Use the Newton-Raphson to find a root of the equation x3 = -cos x. Use an initial guess of x, = 1…

A: The given question is solved below.

Q: Calculate for one real root of tấn x = 4x with X0 = 1.2 up to four decimal places using the…

A: This is a problem from Numerical Analysis.

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.