Question

**Find the root of the function: f(x)=2x+sin(x)-e^x,
using Newton Method and initial value of 0. Calculate the
approximate error in each step. Use maximum 4 steps (in case you do
not observe a convergence).**

Answer #1

Find the root of the function given below that is greater than zero with the Newton-Raphson method. First guess value You can get x0 = 0
f (x) = x2 + x - 2

Using Matlab, find an approximation by the method of false
position for the root of function f(x) = ex −x2 + 3x−2 accurate to
within 10−5 (absolute error) on the interval [0,1]. Please answer
and show code.
Pseudo Code for Method of False Position:
Given [a,b] containing a zero of f(x);
tolerance = 1.e-7; nmax = 1000; itcount = 0; error = 1;
while (itcount <=nmax && error >=tolerance)
itcount = itcount + 1;
x= a - ((b-a)/(f(b)-f(a)))f(a)
error =abs(f(x));...

Find the domain of the function f(x) = 2x-6 over (2x-6)square
root x-1

Use intermediate theorem to show that theer is a root of
f(x)=-e^x+3-2x in the interval (0, 1)

using newtons method to find the second and third root
approximations of
2x^7+2x^4+3=0
starting with x1=1 as the initial approximation

Find the average value of the function on the given
interval/
f(x) = 2x^2 . e^(2x) , [0,1]
the average value is ………… ( round to 3 d.p)

Let f(x)=sin(x), where x is measured in radians.
Calculate f^' (x=0.9) using h=0.1 h=0.01 h=0.001 Calculate the
error using the value of cos(x=0.9). Use f^'
(x)≈(f(x+h)-f(x-h))/2h.

Let F(x) = 1 − e −2x for x > 0 and F(x) = 0 for x ≤ 0. Is
F(x) a distribution function? Explain your answer. If it is a
distribution function, find its density function.

Use Laplace Transform to solve the initial value
problem
x''+2x'+2x=e-t x(0)=x'(0)=0.

2. (a) For the equation e^x = 3 - 2 x , find a function, f(x),
whose x-intercept is the solution of the equation (i.e. a function
suitable to use in Newton’s Method), and use it to set up xn+1 for
Newton’s Method.
(b) Use Newton's method to find x3 , x4 and x5 using the initial
guess x1 = 0 . How many digits of accuracy are you certain of from
these results?
(c) Use x1+ ln 2 and show...

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