Show analytically that Newton's method in the form 1. (141 – 50z2) 94 can be used to estimate v0.94. Use this form of Newton's method, with zo = 1 to estimate v0.94 subject to a tolerance |Zn+1-Inl < 10-4 (All computations at every stage of evaluation should be expressed correct to 5 decimal places).

Q: If third differences are constant, prove that 2 f' f(x) dx = 3 [ƒ(0) + ƒ (1/√2) + ƒ (− 1/√2 )]

A: Hence the answer..

Q: Note that 1/4 ≠ 1/2; but (1/4)^(1/4) = (1/2)^(1/2). Use the hint "y = x^x" to prove that there…

A: Please check next step for details.

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: If ƒ(x) = (6x² – 3)¹, find: f'(x) = ƒ''(x) =

A:

Q: 14. Find the root of f(x) = e¯* – x correct to two decimal places using fixed point iteration…

A:

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)&lt;0 and f(b)&lt;0.…

Q: Compute for a real root of 2 cos x – sin vx = i accurate to 4 significant figures using Fixed-Point…

A: 2cosx3-sinx=14  compute for a real root of equation using fixed point iteration method with an…

Q: solve the following function F(x)=x+e^-x By using these methods: 1) fixed-point 2) Bisection 3)…

A: Fixed-Point Method: To solve F(x) = x + e^(-x) = 0 using the fixed-point method, we can rewrite the…

Q: Use Bisection Method to find the root of f(x)=x^3-3x^2-6x+8=0 near x=3.5

A: x=4 is a root of f(x) =0

Q: 2. Compute for a real root of sin -x 0 using three iterations of Fixed- Point Iteration Method with…

A:

Q: f(x) = x sinx – 4 A. Find the root of this function in between the interval [6 , 7] using the…

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Q: 2. Compute for a real root of sin va - x = 0 using three iterations of Fixed-Point Iteration Method…

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Q: 2. Use Newton-Raphson Method to find the root of x'-2x²-5 = 0 between [1, 4] accurate to five…

A:

Q: 4. Determine one real root of 8 (sin x) e-a – 1 = 0 with Xo = 0.30 using Newton-Raphson Method until…

A: Given, f(x)=8(sin x) e-x -1 We have to find one real root of given function using Newton-Raphson…

Q: Use Newton's method to approximate the maximum of f(x) = 2 sin x- with initial guesses of x = 2.5.…

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Q: Using the Fixed-point iteration method, find the roots of the function: f(x) = x^4 - 20x^2 + x a).…

A: The given function is f(x)=x4-20x2+x. To Find: the root of the function using fixed point iteration…

Q: Q1 Approximate the positive root of the equation x – sinx-1=0 , by performing five iterations of the…

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Q: Use variation of parameters to find the general solution of x' = Ax + f where 433 A =e¹[¹] f = et

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Q: What happens when you try to approximate V3 by using fixed point iteration of g(x) = 3/x?

A: To determine what happens when 3 is approximated using fixed-point iteration.

Q: Compute for a real root of 2 cos √x - sin √x = 4 accurate to 4 significant figures using Fixed-Point…

A:

Q: orward step siz

A: Solution: y=f(x)=sin(0.5x)x

Q: We want to approximate sin x on [-1,1] with an error smaller than 0.00001. What approximation should…

A: The function f(x)=sinx in [-1,1]The error is smaller than 0.00001

Q: Use Newton-Raphson’s method to find solutions accurate to within 10^-4 for each of the following…

A: Newton-Rapson iteration formula is: pK+1=pK-f(pK)f'(pk) here f'=ddx(f) we have f(x)=4e-xsinx -1 and…

Q: Use simple fixed point iteration method to determine the root for 1 (x) = e* – 3x. Assume x, =1 |…

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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.