Using iteration for sequences

Question 1

How to show there is a root in the interval {a.b}

Answer 1

• Show change of sign between f(a) and f(b)

- As f(x) is continuous function and there is a change of sign there must be root {a,b}.

Question 2

What are the exceptions to roots in the interval?

Answer 2

• Negative parabola will have same sign.
• Cubic curve can be more than 1 root.
• Vertical asymptotes

Question 3

How do you solve f(x) = 0 using iterative methods.

Answer 3

-Rearrange into x=g(x) and use formula x+1= g(xn)

Question 4

What are the ways the an iteration can converge?

Answer 4

• Way 1, staircase

- Way 2 cobwebs