$40\%$ Prove or disprove each of the followings.

a$),4n^{2\mathrm{.}5}+n=(100n).$

b$),n^4=(100n^{3\mathrm{.}999}).$

c$),10n^{1\mathrm{.}1}=O(n^{1\mathrm{.}01}).$

d$),O(lo{g}^{2}n)+O(2n)=(n).$

e$)O(logn)=O(10+n^2).$