1. Why is it necessary to measure an algorithms efficiency during the design phase of software, and why is this measurement dependent on the problem size?

2. Determine the big O of each of the following formulas.

f(n) = (n + 1)(n² - 3n)

f(n) = (5n³ + 7n² - 2n + 13) / n

f(n) = (n² + 4)(log(n) + 9) / (n + 3)

3. The following two formulas have equivalent big O values. However, in a practical scenario, which algorithm is likely to be faster? Why?

f(n) = (n² + n) / 2

f(n) = n²

4. Determine the c and N values of the bounding function for each of the following formulas.

f(n) = n! + n³

f(n) = 4n³ + 6n² + 11n 15

f(n) = 3n + log(n)