so, what is confusing you? Newton's method says that, if you have an estimate a root of f(x)=0, you can get a better estimate by using the formula
f(x) -> f(x) - f(x)/f'(x)
You have the function f(x) = x^2-5, so that f(√5) = 0. f'(x) = 2x.
So, you start off with guerssing that x=3. So, the next guess is
3 - f(3)/f'(3) = 3-(9-5)/(2*3) = 2.333
now just keep iterating. A nice web site which shows the steps is
http://keisan.casio.com/exec/system/1244946907
These two q's for my homework I am very confused on how to do:
First Question:
Using Newton’s method, approximate the value of √5 up to 2 decimal points
starting with x1 = 3.
2nd Question:
Thomas Malthus was an economist that predicted that the population grows exponentially while the food supply grows linearly. If p(t) gives the population and f(t) gives the number of people that can be supported by the amount of food produced at t years, we would be concerned about when p(t) = f(t). After this point, the pop. would be beyond capacity that the environment can support. Suppose p(t)= 1000e^(0.02t) and f(t)= 30t + 2000. Using Newton’s method with x1 = 60, find x2 to approximate when the functions intersect.
1 answer
1 answer