Can please do all of the 4 questions in clear steps with an explanation. Thanks

Determine the asymptotic growth of the following functions using big O notation. You do not need to find values of c and no. 1 = + 99n! (a) (5 pts) f(n) = 8Vn 1022 log7(n) (b) (5 pts) f(n) = ()" + n52 (c) (5 pts) f(n) = 512 n log(n+2) (d) (5 pts) f(n) = 25n + 106 (20 pts) For the following pairs of functions, determine the appropriate asymptotic relationship from f to g. The first is provided as an example. You do not need to prove that your answers are correct. g(n) Relationship f(n) = (g(n)) = f(n) n2 ns + 7n2 En? In(n) + 1813 (5)" 13n In(n) + 35_n 1023n7/2 100n5 + 23n4 + 75 + 18n ln(n) n3 + 27n7 + nIn(21n) 52!. 6.022 1023 201 + 1010 Consider the following pseudocode. function f(n) k = 0 for i from 1 ton j = 1 while j