Lett be the 7th digit of your Student ID. Answer each of the following questions: (a) [5 MARKS] Find the limit of the following sequence: et n³ In = t² + 3n+ (t+1)n³ (yn) ². Define the sequences yn = en [in(1)-In(t+2)] and qn = (b) [4 MARKS] If yn converges to I, where does qn converge to? Write your answer in terms of 1. (c) [5 MARKS] Define a subsequence an by choosing every second element of yn (i.e. ak = y2k). Write down the first 4 elements of an. Where does this subsequence converge to if yn converges to ? Write your answer in terms of 1. (d) [8 MARKS] Prove the following statement: A sequence can have at-most one limit. (e) [8 MARKS] Argue whether ak and qn can converge to two different limits. Using your conclusion, calculate the value of the limit 1.