Please show steps on how you achieved the answer. Thank you so much for your help and appreciate your time!

STUDY PROBLEM 1 Show that a) n3+3n2+n+1-9n3) b) n.3-n+1-6(r) In both cases, you need to show that there exist constants no, c1 and c2 as specified in -notation definition. STUDY PROBLEM 2 a) Describe the difference between the and O notation. b) Assume the running time of a function is T(n)-n log n. Which of the following are true and which are false T(n) = 0(n), T(n) = 0(n log n), T(n) = O(n2), T(n)- (n), T(n) = (n log n), T(n) = (n) c) Is 2n+1 = 0(29 true? What about 22n-0(2") ? STUDY PROBLEM 3 Analyze the time complexity of the algorithm below. Use the Big-O notation: T(n)-0(?). Provide justification for your result. BubbleSort (A, n) for (i=1;i=i+1;j--) swap (A [j-1, A[j]) STUDY PROBLEM 1 Show that a) n3+3n2+n+1-9n3) b) n.3-n+1-6(r) In both cases, you need to show that there exist constants no, c1 and c2 as specified in -notation definition. STUDY PROBLEM 2 a) Describe the difference between the and O notation. b) Assume the running time of a function is T(n)-n log n. Which of the following are true and which are false T(n) = 0(n), T(n) = 0(n log n), T(n) = O(n2), T(n)- (n), T(n) = (n log n), T(n) = (n) c) Is 2n+1 = 0(29 true? What about 22n-0(2") ? STUDY PROBLEM 3 Analyze the time complexity of the algorithm below. Use the Big-O notation: T(n)-0(?). Provide justification for your result. BubbleSort (A, n) for (i=1;i=i+1;j--) swap (A [j-1, A[j])