sec asymptotic analysis rule ( says that given two parts of program run in sequence (whether two statements or two sections of code)you need consider only the more expensive part this rule applies to ohm and th notations as wellfor bothyou need consider only the more expensive part rule ( is used to analyze simple loops in programs if some action is repeated some number of timesand each repetition has the same costthen the total cost is the cost of the action multiplied by the number of times that the action takes place this rule applies to ohm and th notations as well taking the first three rules collectivelyyou can ignore all constants and all lower-order terms to determine the asymptotic growth rate for any cost function the advantages and dangers of ignoring constants were discussed near the beginning of this section ignoring lower-order terms is reasonable when performing an asymptotic analysis the higher-order terms soon swamp the lower-order terms in their contribution to the total cost as becomes larger thusif ( then (nis in ( the term contributes relatively little to the total cost throughout the rest of this bookthese simplifying rules are used when discussing the cost for program or algorithm classifying functions given functions (nand (nwhose growth rates are expressed as algebraic equationswe might like to determine if one grows faster than the other the best way to do this is to take the limit of the two functions as grows towards infinityf (nng(nlim if the limit goes to then (nis in ohm( ( )because (ngrows faster if the limit goes to zerothen (nis in ( ( )because (ngrows faster if the limit goes to some constant other than zerothen (nth( ( )because both grow at the same rate example if ( log and (nn is (nin ( ( ))ohm( ( ))or th( ( ))because log log we easily see that log lim