## rate of convergence

hi
im not sure if this topic goes in this part of the forum, but here goes.
doing exam revision and currently stuck on something.

- Bisection method's rate of convergence is 1 (with error constant 1/2).
- Newton's method's rate of convergence is 2 (to find this Taylor expansion is used)

could anyone tell me briefly..
-how to find the rate of convergence?
there is a formula for it, though i am confused on how to apply use it
if you were asked to apply the formula to any problem, how would you go on about it?? because it seems to me every problem is tackled differently (i.e. bisection and newton)
-how would you know when you must use taylor expansion ?