Numbers and definitions

Question 1

Natural numbers are

Answer 1

Positive whole numbers

Question 2

What is a convergent series?

Answer 2

A geometric sequence that homes in on a number, where you can find the sun to infinity

Question 3

What are divergent series?

Answer 3

A geometric series where the numbers get infinitely big, there is no sum to infinity. E.g where a = 2 and r= 2

Question 4

When square rooting, quad rooting etc, what must you put in front of the answer EVERY TIME?!

Answer 4

+-

Question 5

How do you find the root between a and b?

Answer 5

F(a) and f(b)

If the sign changes there is a root! Check the graph too

Question 6

What are upper and lower bounds when trying to find out if a value of x is a root?

Answer 6

The numbers that round to that particular value. 
E.g if x=2.15
Try f(2.145) and f(2.155)

Question 7

What is the iterative method?

Answer 7

When you rearrange a function so that x is on one side alone (you should end up with a square root).
Then you plug in x0 to find x1, then x1 to find x2 etc
This is to find an APPROXIMATION of a root

Question 8

What two conditions must be met for the iteration formula to work?

Answer 8

x0 must be close enough to the root

The derivative must be small at a
E.g |f’(x)| < 1

Question 9

When can the Newton-Raphson formula stop working?

Answer 9

When dy/dx is close to or equal to 0

Question 10

When interpreting using the trapezium method, what is meant by ordinates?

Answer 10

This is the number of y values, it’s basically n + 1

For example, 4 strips is 5 ordinates