How did the experience of living under british
rute influence the attitude of amercans
toward limited gov. and the rule of law?

Their experience was bad and they did not liked at all of a limited government,  and this changed their views of how to be a better society and to have better laws.

The concept of the rule of law is related to state power. That is when this power, in relation to the decisions that can be made by the rulers, is limited by the set of laws, by the law.

In the rule of law, all fundamental human rights must be protected by the state: political, social and economic rights.

Law, through legislation, will define what can and cannot be done, both for rulers and for citizens. In the rule of law a decision cannot be contrary to the law, ie the law cannot be violated.