Obtain a quadratic polynomial approximation to f (x)= 3e* using Newton divided difference interpolation method, taking x= 0, 0.5, 1. Also find ƒ (0.8) by using it.

Q: Show that f(x) = x^3 + 3x^2 - 5 has only one zero in [1,2]. Then use the Newton's method to…

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Q: Estimate the root of following nonlinear equation x – 2x – 1 = 0 using Newton-Raphson method…

A: (a) The given equation is f(x)=x4-2x-1=0 find the derivative f'=4x3-2 initial guess x0=-1…

Q: Compute for a real root of Sin Vx – x = 0 using three iterations of Fixed-Point Iteration - Method…

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Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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Q: 2. Find the root of f (x) = 2* + x³ – x = 0 by using Newton Raphson method with initial value po=…

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Q: Find a root of the set of equations around the point x0 = 0.6, y0 = 1.5 by the Newton-Raphson method…

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Q: 6. Use an appropiate linear approximation to estimate the value of In(1.01). Compare your…

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Q: Find the maximum of f(x) = 4x − 1.8x2 + 1.2x3 − 0.3x4 USING Newton’s method (x0 = 3, εs = 1%)

A: Given: f(x) = 4x − 1.8x2 + 1.2x3 − 0.3x4 x0=3, εs = 1% Fomrula used:

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A: The function fx,y=11-3x-y Then the taylor's formula for fx,y is, fxx,y=31-3x-y2fyx,y=11-3x-y2 Then…

Q: 1. Find an estimate of the root of the equation: 3 = 5x2 located in the interval (0,1) using…

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: f(x)=x3-7x²+8x-3 iF Xo =5

A: Using Newton-Raphson Method we determine the approximation to the solution, where  f(x)=…

Q: f(x) Vx+1

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Q: Use Euler method to approximate the value of y(0.1), given y' - x2 - y = 5, y(0) = 3 with Ax = 0.025…

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Q: Calculate the real root of f(x)=x^3-2x^2-2x-1.9 with the first iteration of Newton-Raphson method.…

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Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: 2. Find the root of f(x) = 2* +x³ – x = 0 by using Newton Raphson method with initial value po= -1,5…

A: Consider the provided question, fx=2x+x3-xWith initial value p0=-1.5  and…

Q: Use an appropiate linear approximation to estimate the value of In(1.01). Compare your approximation…

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Q: If Newton's method is used to find the critical number of f(x) = x® – x³ +x² – 2x with initial…

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Q: Determine the root of the equation x³ + x² = 1 in the interval [0, 1] by using bisection method.

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Q: Determine the real root of f(x) = 3x^3 + 2x + 6. Iterate until the estimated error falls equal or…

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Q: Use Newton's method to approximate the indicated root of f(x)= xª + x – 4 in the interval [1,2]…

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Q: Find the smallest positive root by using fixed- point method f (x) = In(3x)– x² +2 %3D with three…

A: Given: fx=ln3x-x2+2. We have to find the smallest positive root by using fixed-point method with…

Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x' +4x +1

A: f(x) = x5 + 4x + 1 Basic formula for Newton's Method is: xn+1 = xn - fxnf'xn f'x = 5x4 + 41 + 0 =…

Q: Write the formula for Newton's method and use the given initial approximation to compute the…

A: The solution is given below

Q: Use Newton's method with the specified initial approximation x1 to find x3, the third approximation…

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Q: Use Newton's method to approximate the indicated root of x*+x-9 = 0 in the interval [1, 2], correct…

A: According to Newton's method, the root of some equation f(x)=0 can be obtained by: xn+1=f(xn)f ' xn…

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

Q: Find the approximate root of function f (x) = 0.48x³ - 2.7x - 5.36 by using the newton raphson…

A: Given function fx=0.48x3-2.7x-5.36             ……………………1 Initial guess x0=3.5

Q: Find atleast three approximations of a solution of the equation f(x) = x – 2x3 0 by Newton Rampson…

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Q: Find the smallest positive root by using fixed-point method f(x) = In(3x)– x² +2 with three…

A: we have f(x)=ln(3x)-x2+2=0 x2=ln(3x)+2x=ln(3x)+2using fixed point iterationxn+1=ln(3xn)+2take…

Q: Find the rod of greatest length that can be inserted between y= square root of x and y=x^3…

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Q: Approximate the zeros of f(x) = 2x³ + x² − x + 1 using Newton’s Method. Present each iteration in…

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Q: The 2nd approximation to the real root of the equation x³ – x² – 1 in the interval [1, 2] using…

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Q: Find all the possible roots of the function f(x) = x3 + x – 1, by using Fixed Point Iteration…

A: Fixed point iteration method: The equation f(x) = 0 can be converted algebraically into the form x =…

Q: : Find a root of x- 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that the…

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Q: What is the second iterative value of the root f(x) = x2 - 3. with the initial bracket [1, 2] using…

A: To find The second iterative value of the root of f(x) using the bisection method.

Q: f(x) = x - e-x?

A: Use bisection method to find a root.

Q: Consider the function f(x) = x³ + 2x + 5. Estimate the root to eight significant digits using Newton…

A: The general form of an equation of degree 3 is given by ax3+bx2+cx+d=0, where a≠0. In this problem,…

Q: Find one of the roots of the function using Regula-Falsi method. £ (x) = x- V+1

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Q: Find the quadratic approximation to ƒ(x) = 1/(1 - x) atx = 0.

A: Given,  f(x) = 1/(1 - x) at x = 0

Q: Find X1 & X2 using Newton's method to minimize x2 – y2/2 starting from (1,1)

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: Estimate the In (1.1) and sec (0.1) Using a linear approximation and without using any kind of…

A: f(x)=ln(x) f'(x)=1/x f(1)=ln(1)=0 f'(1)=1/1=1 linear approximation is then L(x)=f(a)+(x-a)f'(a)…

Q: Let -(x) be the Taylor polynomial of degree for the function x) = cos(x) at = 0. Suppose you…

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Q: Consider the function f(x) = 2/x. Calculate the second derivitave at x = 2 numerically using central…

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Q: Estimate the root of the expression, f(x) = x* – 4x, using: a. Bisection Methodin the interval [0,2]…

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

Q: Use Newton's method to estimate the one real solution of x° + 3x + 1 = 0. Start with x, = 0 and then…

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Q: Use Newton's method with initial guess x0 = 1 to compute two successful approximations of x3-2= 0.

A: Please see the answer below

Q: Find atleast three approximations of a solution of the equation f(x) = x – 2x = 0 by Newton Rampson…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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.