4. Determine which grows faster (in each case, show the steps for your choice) (30 points): For (a) to (e), provide your analysis using L'Hopital's Rule N 2-5 log N or log N +N3 Nk+8 + Nk logN or k Nk+8 with the constants k , &>0 N 2 or (N + log N) 2N-1 n + n logn or n log n log N or N1/2 n! 2" (Use Stirling's approximation for n! for n large) or 4. Determine which grows faster (in each case, show the steps for your choice) (30 points): For (a) to (e), provide your analysis using L'Hopital's Rule N 2-5 log N or log N +N3 Nk+8 + Nk logN or k Nk+8 with the constants k , &>0 N 2 or (N + log N) 2N-1 n + n logn or n log n log N or N1/2 n! 2" (Use Stirling's approximation for n! for n large) or