Q.4. Determine the negative root of: f(x) = x' – x² - 5x – 3 using the most suitable Newton-Raphson method and an initial guess of x=0.45. Stop iteration when ɛ < 0.5 % is satisfied.

Q: Q5/ Determine the positive root of f(x) = x¹0 - 1 using the Newton-Raphson method and an initial…

A: The function is given as f(x)=x10-1. We have to find the positive root of the function using…

Q: 1) a) Derive the secant method to solve for the roots of f(x)=0 nonlinear equation, b) Use the…

A:

Q: Q1-Find dy / dx for the following functions : * -2 2.8ln2 Cosh9x, * Inxy 2 Y= 4 3 6. sino 5 log22…

A: We have to solve given problem:

Q: Use two iterations of the Newton-Raphson method with a st solution to the equation: f(x) = e-5æ = 0.…

A: Introduction: The general formula of newton-raphson method is given by, xn+1=xn-f(xn)f'(xn)

Q: 1. Use Euler iterative technique to solve = (xy)² for y(0)=2 with h=0.5, find y(2) dx

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

Q: 2- Determine the root of the below equation ), [use four decimal places in your all answers and…

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Q: Solve the following initial value problem (t2-22t+105)(dy/dt)=y with y(11)=1 Find y as a function of…

A: According to the given information it is required to solve the given initial value problem:

Q: Consider the initial value problem: y (t) = cos(y(t)) + y(t)t³ – 4 with y(-1) = b. If Euler's method…

A: Given the initial value problem y't=cosyt+ytt3-4  with y-1=b and n=10

Q: 3. For the equation: t(3+ +100 = e-t a- Using a spreadsheet, plot the function f(t) from t = 0 to t…

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Q: Q1: Use 2 iterations of the Newton-Raphson method to approximate the solution to x' +y' = 5 y – x' =…

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

Q: Q5; Use three iteration of Picard's method to solve = 3x+ y' when x=0.1, given that y 1 dx for x=0.

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Q: The following ordinary differential equation is given: d^ 2u /dx^ 2 + 6 du /dx – u = 2 At x = 0, u…

A:

Q: Q3: Find solution of following initial value problem using Euler method f(x,y) = x-2y + 3, y(0. 1) =…

A: As you didn't provide h, we take h=0.1

Q: Q1 Use Modified Euler's method without iterations to solve the ordinary differential equation at the…

A: Modified Euler's method uses the formula: ym+1=ym+hf(tm+12h,ym+12hf(tm,ym)) to approximate the value…

Q: Q5: Use Euler method to solve the following O.D.E. ý = 3- x² + y² With the initial condition y(0) =…

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Q: Q3: Use two iterations of Newton-Raphson method to solve the following nonlinear equation sin? (x) +…

A:

Q: Q5:al Using the Runge-Kutta method, solve x = 0.2 when h = 0.2. dy = x + y² with the initial…

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

Q: Q2/Solve the following equation from t=0 to 1 with step size is 0.5 using E Method. dy -= y sin³ (t)…

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Q: 1. Employ the Heun's method to solve x .y=1, using a step size of 0.7 and y(1)=5 dx and determine…

A:

Q: Q5: Use Euler method to solve the following O.D.E. X • y ý = 3 Vx2 + y2 With the initial condition…

A: Define: f(x,y)=y' Given:      y'=3xyx2+y2     initial condition y0=2 , interval 0,1    step size…

Q: Consider the IVP: x" +3(x')2 + 10tx = 0, x(0) = - 3, x'(0) = 2 Using the Euler method with a time…

A: Given x''+3x'2+10tx=0, x0=-3, x'0=2, ∆t=0.5

Q: Consider the initial value problem: y'(t) = sin(t) – tVy(t). y(0) = 1. Use the improved Euler's…

A: Given initial value problem is  y'(t)=sin(t)-ty(t),    y(0)=1

Q: Which of the following should the function k(x) be in order for the solution of differential k(x) 2…

A: Given that. The solution of the differential equation To find The value of k(x).

Q: 1-cos (t) B: Solve the D.E ý + 2ý + y = with zero initial conditions

A: Given y''+2y'+y=1-costt2with zero initial condition, i.e. y0=y'0=0

Q: (64 – 2) dy = 1, y(0) = 9 Solve the initial-value problem for y as a function of x. %3D da

A: We need to solve the initial-value problem 64-x2 dydx=1, y0=9 for y as a function of x. So,…

Q: (c) (5) Give an example of a function g and an initial value ci such that the Newton-Raphson method…

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Q: Solve the following initial value problem by the 2nd order and 4th order Runge-Kutta methods,…

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Q: Find the third iteration value of an extremum (maximum/minimum value) of z F4.png f(x) = In(ax + 25)…

A: Newton's method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations. The initial value…

Q: Solve for the only positive value of x that satisfies the equation **-1 = -√(1-e-*) Using the…

A: Given that: xx-1=121-e-x Using a tolerance of 0.0001. Now solving, Let using the Bisection method,…

Q: Q1: Use 2 iterations of the Newton-Raphson method to approximate the solution to x' +y* = 5 y – x' =…

A: Given: The given equation is x2+y2=5 ⇒x2+y2-5y-x2=-1⇒y-x2-1

Q: Solve the following problem over the interval from x=0 to 1 using a step size of 0.25 where y(0) = .…

A:

Q: Approximate the solution of the equation x² – In(sinx) – 5 = o in the 3rd iteration of the Newton…

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Q: 2. The table on the right gives the value of x(t 1) from numerical integration of the equation: Δt…

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Q: Fird X1 value for solving fox=-€Xx² by considering the Newton Raphson Method foronly first iteration…

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Q: Q-the Newton raphson method is applied to find the root of f(x)= x* -1 with an initial guess Xo =0.5…

A: Given function is, fx=x2-1......(1)fxn=xn2-1....2 Differentiating the equation (1) up to first order…

Q: For the following initial value problem, compute the first two approximations u, and u2 given by…

A: Introduction: Euler's method is a basic tool to solve a first-order differential equation…

Q: Find the solution of the following nonlinear equation x-e* = 0 using the Newton method, start with…

A:

Q: Q-the Newton raphson method is applied to find the root of f(x)= x² -1 with an initial guess xo =0.5…

A:

Q: (a) Integrate x ln(x + 1)dx analytically; and numerically using (b) trapezoidal rule with iterations…

A: As per the rules we can solve only 3subparts per questions so I'm solving a,b,c

Q: Find the third iteration value of an extremum (maximum/minimum value) of z F1.png f(x) = In(ax + 25)…

A: Given that,fx=lnax+25+bx3-cx+23xThe third iteration of an extremum of the function is determined as…

Q: 10-Which of the following is the approximate solution of x^3 – 3 = 0 using the Newton-Raphson method…

A: Newton Raphson method Steps (Rule) Step-1: Find points a and b such that a&lt;b and…

Q: 1. Given an IVP y' = f(x,y), y(1) = y0, how many iterations of Euler’s method needs to be applied to…

A: The Eulers method states that: yn+1=yn+hfxn,yn The value of h=0.05, therefore to calculate the value…

Q: Q1: Use 2 iterations of the Newton-Raphson method to approximate the solution to x' +y' = 5 y -x =…

A: The functions will be:  fx,y=x2+y2-5=0 gx,y=y-x2+1=0

Q: 1. Find the roots of S(x, y) = x' -x*y- 20 g(x, y) = y - xy' + 60 with initial guesses of x, = y, =…

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Q: . Apply to the initial value problem y' = -xy + 1, y(0) = 0 three steps of the Picard-Lindelöf…

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Q: Approximate the solution of the equation x2 – In(sinx) – 5= 0 in the 3rd iteration of the Newton…

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Q: The first approximation P of the solution to the equation f(z) = x² – 8 that is near to Po = 4 using…

A: As we know that the iteration formula of Newton's method is:   Pi+1=Pi-fPif'Pi  i=0,1,2,3.....…

Q: 3 Q2. Find an approximation to V11 using 4 steps Newton's method.

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Q: Q1: Use Newton - Raphson method to estimate the 3 Yoot of fcx) = x-X-1, employing an initial guess…

A: We have to use Newton-Raphson method which is widely used in finding the root of nonlinear…

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.