Pure Year 2 Unit 10

Question 1

If the function f(x) is continuous on the interval [a, b] and f(a) and f(b) have opposite signs, then what?

Answer 1

f(x) has at least one root, x, which satisfies a

Question 2

To determine a root to a given degree, use 1.763 as an example

Answer 2

If there is a change in sign for the upper and lower bound

e.g. 1.7635 and 1.7625 has a sign change

Question 3

How can roots converge?

Answer 3

Stair case or spiderweb

Question 4

What is the newton-raphson formula

Answer 4

X(n+1) = X(n) - (f(x(n)) / f’(x(n)))