- < < / so as lim / naehence ( for = and >no= example show that ( solution by the definitionwe can write <cg( < ( <cn < dividing by we get / <cn / < / < < / thusfrom the above statementwe see that the value of depends on the value of there does not exist value of that satisfies the condition as increases this could fairly be possible if but it is not allowed as the definition by itself says that lim nae theta notation (qtheta notation provides an asymptotically tight bound for (nth notation is simply written asf(nth( ( ))where is the problem size and th( ( ){ ( )positive constants and such that hencewe can say that th( ( )comprises set of all the functions (nthat are between (nand (nfor all values of > if (nis between (nand ( ) > then (nth( ( )and (nis an asymptotically tight bound for (nand (nis amongst (nin the set to summarizethe best case in th notation is not used worst case th describes asymptotic bounds for worst case combination of input values if we simply write thit means same as worst case th example show that / th( solution by the definitionwe can write ( < ( < (nc < / < dividing by we get / < / / < / < / / < this means / because lim / / / (big notationnaeto determine using notationwe can write < / / we see that is minimum when therefore < / / hencec / now let us determine the value of / < / / < / / < / / < / / < / < /