7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.

15x4- 13x2+ a is o(x*). Hint: Apply theurem I. x"+1 is o(x). Hint: Use lng divisinm. 2. i"+a+3"+ --- +n" =(n"). Hint: For n>! 4 4 3. +n = O(n'). Hìnt: For n>I *sn)くn"etc 4. 2*+17 is O(3") . * , Hint: 2く3 and 17<3*, X23 5. Carefully explain what is by meant 6. Find n where (x²+ ax+1)* is o(X). Hint: expand (x*+ax+U and apply theorem 1.

Compute limn→∞n (√4n²+3 - 2n) and justify your calculations.

9. Determine whether f is injective, surjective or bijective. 마 5 d. Suppose f : N → N has the rule f(n) = 4n2 + 1. e. Suppose f : R → R where f(x) = [x/2].

Prove this proposition algebraically

Calculate ∪∞n=1 An and ∩∞n=1 Anwhere for each n ∈N the set An is defined as:                                                           (vii) An= [−1, 3 + (1/(n) ] ∪ [5, (5n + 1)/(n) )(viii) An= ( (−1/(n)), 1] ∪(2, (3n −1)/(n) ]