Big-O estimate (smallest order)

Question

I'm trying to give a big-O estimate for each of these functions, where I want to use a simple function $g$ of smallest order. I have them all done I just wanted to someone to run through and check them because I am confused on a few.. If one is wrong could you please explain why.

a) $6x^4+3^x+12 = O(x^4)$

b) $2+4x+8x^2 = O(x^2)$

c) $(x^3+2x)/(2x+1)= O(x^3)$

d) $\log x+27 = O(\log x)$

e) $(2^x+x^2)(x^4+3^x) = O(x^6)$

Answer 1

e) is incorrect. Exponentials trump powers at infinity. (2^x) * (3^x) = 6^x, therefore e) is O(6^x).