For the equation e^x =x+2,
(a) use the fixed point iteration method to determine its two roots
to eight correct decimal places (you may need to write this
equation in two different ways of x = g(x) in order to obtain these
two roots);
(b) numerically calculate the convergence rates for your converged
iterations; (c) compare these numerical convergence rates with the
theoretical conver- gence rates we presented in class (also see
Theorem 1.6 on page 38 of the textbook).
Use the False Position method to find a guess of the root of
f(x) = cos(x2 ) with lower and upper bounds of 0 and 2,
respectively. Then, narrow the interval and find a new guess of the
root using False Position. What is your relative approximate
error?
a. 8.47% answer
b. 12.45%
c. 0.112
d. 0.243
e. None of the above
Please provide complete solution how the answer is
a
thumbs up for correct and neat solution! step by...
Use a fixed-point iteration to determine the solution (in
[0,1])ofthe equation x = 1.5cos(x). Use a starting value of 0.5.
How many iterations does it take before you have an answer which is
accurate in the first 2 digits? ...in the first 3 digits?...in the
first 4 digits? What happens if you change the starting value to
0.7?...to 0.0?
Does the fixed-point iteration converge? If not, modify the
equation so that x = cos(x)/30 + 44x/45. Does the iteration
converge...
Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find
and simplify expressions for the following functions and state the
domain of each using interval notation. a . (h ? g ? f)(x) b. (h ?
f ? g)(x) (g ? f ? h)(x)