1) Let A and B be two programs that perform the same task. Let tA (n) and tB (n), respectively, denote their run times. For each of the following pairs, find the range of n values for which program A is faster than program B. Show the values for each and how you obtained them (justify).

a) tA (n) =1000n , tB (n) =10n^2

b) tA (n) = 2n^2 , tB (n) = n ^3

c) tA (n) = 2^n , tB (n) =100n

d) tA (n) =1000n logn , tB (n) = n^2