Itteration

Question 1

To check if x0 gives a good second approximation using Newton-Raphson, what do you do on the diagram ?

Answer 1

Start at x0 on the x-axis, go up to the curve y=f(x), draw the tangent at that point, and see where it hits the x-axis — if it lands close to the actual root, it’s a good approximation.

Question 2

For graphical iteration, what do we hit first

Answer 2

Draw Y=x
Start at X0
Go up to curve then horizontally to line and repeat

Vertical move → curve

Horizontal move → line

Repeat

(Can then move up or down left or right to hit curve and line respectively)

Question 3

If there is alpha is 0.889 to 3dp, what is the interval we check

Answer 3

[0.8885,0.8895]

Both 5 up and down at the end