2. For this problem, you need to base your answer on the definitions of the asymptotic notations. 1. (10 points) Show 8n3logn+14n2=(n3logn) 2. (10 points) If f(n)=O(g(n)), can we conclude If 2f(n)=O(2g(n)) ?, Justify your answer. (20 points) Sum of two numbers You are given an array A[1n] of arbitrary integers and another integer u. The problem is to check if the array A has two elements x and y such that x+y=u. Present an algorithm to solve this problem. What is the run time of your algorithm? Note: you should try to design an algorithm that is more efficient than the simple brute-force algorithm