Question

Use the bisection method to find roots for the following function on the intervals indicated:

h(x) = x + 10 - x cosh(50/x), on [120,130]

Answer #1

Use the Bisection Method to locate all solutions of the
following equations. Sketch the
function by using Matlab’s plot command and identify three
intervals of length one that
contain a root. Then find the roots to six correct decimal places.
(a) 2x3 − 6x − 1 = 0
(b) ex−2 + x3 − x = 0 (c) 1 + 5x − 6x3 − e2x = 0
**MUST BE DONE IN MATLAB AND NEEDS CODE

Consider the function f(x) = 1 2 |x|.
a) Can we use bisection search to find one of its roots? Why or
why not?
b) Can we use Newton’s method to find one of its roots? Why or
why not?

The given equation has a root in the indicated interval.In
MatLab, use the Bisection method to generate the first four
midpoints and intervals (besides the original interval given)
containing the root.
equation: e^x - 2x= 2,[0,2]

Answer each of the following in details~:
(a) Can the Bisection method be used to find the roots of the
function ?(?) = 1 + ??? ?? Justify your Answer.
(b) While using the Newton’s method with the initial guess ?0 =
4 and ?(?0) = 1 gives ?1 = 3. Find ?′(?0).
(c) While using the Secant method for finding a root, ?0 = 2, ?1
= −1, ??? ?2 = −2 with ?(?1) = 4. Find ?(?0).

for f=(x^4)-(6.4*x^3)+(6.45*x^2)+(20.538*x)- 31.752;
find the roots using bisection for five iterations

1- Let the bisection method be applied to a continuous function,
resulting in the intervals[a0,b0],[a1,b1], and so on. Letcn=an+bn2,
and let r=lim n→∞cn be the corresponding root. Let en=r−c
a. 1-1) Show that|en|≤2−n−1(b0−a0).
b. Show that|cn−cn+1|=2−n−2(b0−a0).
c Show that it is NOT necessarily true that|e0|≥|e1|≥···by
considering the function f(x) =x−0.2on the interval[−1,1].

Using the secant method, find the roots of the following.
x=e-x. Carry out the method to find three
approximations.

find solution bisection method
x^2-5x+2 limit 3%

Q1: Use bisection method to ﬁnd solution accurate to within
10^−4 on the interval [0, 1] of the function f(x) = x−2^−x
Q3: Find Newton’s formula for f(x) = x^(3) −3x + 1 in [1,3] to
calculate x5, if x0 = 1.5. Also, ﬁnd the rate of convergence of the
method.
Q4: Solve the equation e^(−x) −x = 0 by secant method, using x0
= 0 and x1 = 1, accurate to 10^−4.
Q5: Solve the following system using the...

The indicated function y1(x) is a solution of the associated
homogeneous differential equation. Use the method of reduction of
order to find a second solution y2(x) and a particular solution of
the given nonhomoegeneous equation.
y'' − y' = e^x
y1 = e^x

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