Please double check your work. Thank you.

Give the answer for the two problems below and justify your answer using the limit theorem and computing the actual limit. Saying: "The limit is x because this term dominates the other" is not a valid proof. To clarify, You can use the 'dominant term' argument when you talk about polynomial terms (i.e. n^d). a) is 2^n+1 = O(2^n)? b) is 2^2n = O(2^n)