Please answers these questions

Answering and Submission: You should answer in the space provided. Either type your solutions or scan your answers and include the scanned picture file in the space provided in the document and submit (upload in Canvas) the entire exam as a single word document or PDF file. Note: You should NOT use any actual programming code (in C++, Java, etc) to answer the questions. If you do so, you will get only a ZERO for the question. Q1) (5pts) Let T(n)=7T(n/2)+3n2+2. Using Master Theorem and the Limits approach, show that T(n)=O(n3) Q2) (5 pts) Let T(n)=3T(n/4)+nlogn. Solve the recurrence using Master Theorem. Q3) (15 pts) Consider the array assigned to you. (a) Illustrate the sorting of the array using the Divide and Conquer approach of the Merge Sort algorithm. (b) Determine the number of inversions in the array. Show all the steps. Answering and Submission: You should answer in the space provided. Either type your solutions or scan your answers and include the scanned picture file in the space provided in the document and submit (upload in Canvas) the entire exam as a single word document or PDF file. Note: You should NOT use any actual programming code (in C++, Java, etc) to answer the questions. If you do so, you will get only a ZERO for the question. Q1) (5pts) Let T(n)=7T(n/2)+3n2+2. Using Master Theorem and the Limits approach, show that T(n)=O(n3) Q2) (5 pts) Let T(n)=3T(n/4)+nlogn. Solve the recurrence using Master Theorem. Q3) (15 pts) Consider the array assigned to you. (a) Illustrate the sorting of the array using the Divide and Conquer approach of the Merge Sort algorithm. (b) Determine the number of inversions in the array. Show all the steps