ch10 numerical methods

Question 1

What to do in a question where it says “by choosing a suitable interval, prove that theta = -1.132 to 3dp.

Answer 1

Work out the lower bound (lowest value that it could be rounded to) -1.315
Work up the upper bound (largest value it could be rounded to) -1.325.

Sub in these values for x.
Show that there is a change of sign and this can prove theta.

Question 2

What is the theory that can help find roots in an interval?

Answer 2

if a continuous function f(x) on the interval [a,b] and f(a) and f(b) produce a change in sign there is at least one root in that interval.

Question 3

When may the locating roots theory be inaccurate?

Answer 3

When the interval is too big

When there is a discontinuous function.

Question 4

What could be the exception if there is no change of sign?

Answer 4

-There could be an 2,4,6 any even number of roots.

Question 5

What must you do to a function before you can use it to locate roots?

Answer 5

Put it in the form f(x)=0

Question 6

How do you create an appropriate iterative formula?

Answer 6

Set f(x)=0 
then make x the subject

xn+1 = x