(a) Sketch the function f=inline('x^2 -4') (b) Using graphical method, what is the maximum number of roots that this function has. Choices 2 1 O infinite

Q: i) Find the tangent and normal lines to the curve r*y° +sin(xy)+ln(1+y)+sin(2x) = sin(2) at the…

A:

Q: What is the second iterative value of a root f(x) = x3 - (7/2) + 2. starting interval [1.4, 1.5],…

A: Given: Bisection method: In this method is an approximation method to find the roots of given…

Q: 3.82x5 – 3.23x³ + 1.73x² – 0.83x = 0 -

A: Use the formula of secant method to determine the approximate roots. Determine the iterations till…

Q: Q1. Use Newton-Raphson method to locate the first positive root of f(x) = tanx - 2tanhx = 0

A: In Newton-Raphson method  x0 is the initial solution of f(x) then further solutions are obtained…

Q: A rectangular sheet of metal 360mm by 240mm has four equal squares cut out at the corners. The sides…

A: Volume of the rectangular box= (Length)*(Breadth)*(Height)

Q: An object hangs from a string in a stable position and is represented by the function y = 4 sin (3x)…

A:

Q: The basic idea of optimization is that we have a quantity (represented by a function), and we need…

A: The basic idea of optimization is to find the maximum or minimum of a function using the different…

Q: Find the real root of x2ex= 1 by Newton-Raphson Method. The function is lying between [0.5,1],…

A: Here x2ex-1=0Let f(x)=x2ex-1ddxx2ex-1=2xex+x2ex ∴f'(x)=2xex+x2exHere x 0 1 f(x) -1 1.7183…

Q: Explain why Newton's method doesn't work for finding the root of the equation x3 - 3x +1 = 0 if the…

A: Given that

Q: Using Fixed Point Iteration Method manually, Given: f(x) = x^3 + 3x^2 - 1 and its new function as…

A: The function given is as follows: fx=x3+3x2-1 The new function mentioned can be found as follows:…

Q: The equation for the maximum deflection as a function of x is given by: -0.67665x10x -0.26689x10x³…

A:

Q: How can you find the first derivative of the given polynomial function? What mathematical skill is…

A: Let the polynomial be pn(x)=a0+a1x+a2x2+a3x2+...+anxn Now, the first derivative of the above…

Q: Discuss the method of False position to find an approximate root of an equation f(x) = 0. %3D

A: We have to describe the method of false position.

Q: # 22 A right circular cone of radius 6m and height 10m is initially filled with water. An empty…

A: We know volume of water in cylinder = volume of cone - volume of water remaining in cone

Q: Determine algebraically where the cubic function with zeroes at 2, 3 and -5 and passes through the…

A:

Q: Calculate one of the roots of the equation f(x) = x ^ 3 + x ^ 2 - 2x - 4 = 0 with an error less than…

A:

Q: Approximate the root of the equation f(x) = x^3 - x - 1 using 10 iterations on Bisection Method with…

A:

Q: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

Q: 4. Determine the root of the given function using Secant method. Show the tabulated the results. Use…

A: The secant method uses the formula to perform the iterations and to approximate the root of the…

Q: Example: Use the Secant method to estimate the root of f(x) = e-x-x. Start with initial estimates…

A: To use secant method to estimate the root of fx=e−x−x

Q: The equation for the maximum deflection as a function of x is given by: -0.67665x10x¹ -0.26689×10x³…

A:

Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of f(x) = 5sin2x -…

A:

Q: Find the absolute extrema of the function on the interval [0, 0). (If an answer does not exist,…

A:

Q: 73 9x +4 then f(x) has a local maximum at the point 3 Use second derivative test, If f(x) %3D - O…

A: Topic:- application of derivatives

Q: Determine the multiple real root of f(x) = x - 2xe* +e* using Modified Newton-Raphson Method. Plot…

A: Given: To find the multiple real roots of f(x)= x2-2xe-x+e-2x

Q: #13

A:

Q: 5. Find the absolute minimum and absolute maximum values of f(x)= 2cosx +sin2x on the interval 2 N

A: Consider the given function,To find the absolute minimum and maximum values of the given function,…

Q: Find the third iteration value in finding an extremum (maximum/minimum) value of f(x) = 5sin2x - 4x…

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

Q: 2. Determine the multiple real root of f(x) =x² – 2xe* +e* using Modified Newton-Raphson Method.…

A: Given: To determine the multiple real root of f(x)=x2-2xe-x+e-2x.

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 root between [-1,0] where f (x) = (x+2)³ +2x – 5 with error epsilon=0.1 by using False…

A: The false position method is one of the methods used to find the approximate root of a function in a…

Q: Use Newton's Method to approximate the zero of the function f(x) = x + x - 1. Start with x1 = 0.5…

A: The given function is f(x)=x5+x-1, with x1=0.5

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x)…

A: Let's find.

Q: Find the third iteration value in finding an extremum (maximum/minimum) value of…

A: Given,                 f(x)=5sin(2x)-2x2 and  initial guess of x = -0.38.

Q: Determine the root f(x)=x-2e^-x using newton-raphson method. Start at x1 = 0 and carry out the first…

A:

Q: use newton method to approximate the zero(s) of function continue iteration until two…

A: Given function is fx=x2+x-5. Compute the derivative. f'x=x2+x-5'=2x+1 Newton's method,…

Q: Find a root of an equation f (x) = 4.15x3-2x+5.15 using Incremental search method at a step- size…

A: Given: f(x)=4.15x3-2x+5.15, a=-2 and b=-1 To find: Root of a given equation by Incremental search…

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

A:

Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of              f(x)…

A: The Newton Raphson method is used to solve an equation numerically. When the extremum of a function…

Q: 1. Find two non-negative numbers whose sum is 12 such that their product is an absolute maximum.

A: Let x and y are two non-negative numbers. We have to find maximum of the function Fx,y=xy It is…

Q: 4. The profile of the cables of a suspension bridge may be modeled by a parabola. The central span…

A:

Q: (x) = 5sin2x

A:

Q: A golfer makes a successful chip shot to the green. Suppose that the path of the ball from the…

A: Please refer to the image below

Q: use netwons method to approximate the zero(s) of the function. continue the iterations until two…

A: To find zeros of the below function using Newton's method and graphing utility.…

Q: Using incremental search with x1 = 1.5 and Ax = 0.01, %3D %3D approximate the solution of Inx = =…

A: fx=lnx - 2+xx1=1.5∆x=0.01tolerance=0.05----------------Find: To find 'x=a' such that fa = 0±0.05.…

Q: Using Secant method, the approximation of the root of the function f(x) = xe*-x - 1 %3D accurate to…

A: The given function is f(x)=xex-x-1 And x0=0.7   &  x1=0.76

Q: determine all critical points and all domainendpoints for each function. y = 2√(1 - x2) + sin-1 x

A: Given that, y=21-x2+sin-1x

Q: An open-top box is to be made from a 30-inch by 48-inch piece of plastic by removing a square from…

A:

Q: Use Newton’s method with initial approximation x1 =-1to find x2 , the second approximation to the…

A: Given, the function is x3 + x + 3 = 0, and the initial approximation is x1 = -1, we have to find the…