Please answer the following question and specify your answer whether you are using the positive or negative direction. If you are using big theta,

make sure to answer both Big O and Big Omega in bot h the positive and negative direction.

Big-O Justification Indicate whether the following assertions are true or false, and give a justification: n+5m2+8n is O(n) n!+IFs O(n * log n) Iog n + n * log n + 10g(log n)is (n) . 1/(n) + log32 is (1) 15) + log32 is QI) If you are justifying the positive direction, give choices of ne and C. For big-0, make sure to justify both big-O and big-2, or big-O in both directions. If you are justifying the negative direction, indicate which term(s) can't work because one is guaranteed to grow faster or slower than the other. As a quick guide, here is an ordering of functions from slowest-growing (indeed, the first two shrink as n increases) to fastest-growing that you might find helpful: f(n) 1/(n2) .f(n) log(n) f(n) sqrt(n) f(n) = n f(n)- n2 f(n) n3 f(n)- n4 and so on for constant polynomials . f(n) n