Determine T(n) in terms of a Big Theta notation for the following cases. Use expansion method: T(n) = 2T(n - 1) + 1 T(0) = 0

Apply R to simulate a set of 100 numbers with standard deviation of 2 and mean of 20. List out the set of numbers.

Write a procedure sum-range (from to) for finding the sum of integers in the range from to to, inclusive. Make sure that (sum-range 4 18), (sum-range 18 4), and (sum-range 7 7) all give the expected result. Note that this function should be able to count up or count down depending on the order of the paramaters. So, (sum-range 4 18) and (sum-range 18 4) should give the same result. (sum-range 7 7) should return 7. (Dr.Racket)

Use the substitution method to show that the recurrence defined by T(n) = 2T(n/3) + Θ(n) hassolution T(n) = Θ(n).

What is the right answer and please explain why

1. Use the substitution method to verify that the upper bound solution to the recurrence: T(n) = 3T ([n/4])+(n²) is O(n²). Otherwise, if O(n²) is not the solution, find the correct solution to the above recurrence.

1. Use the substitution method to show the recurrence: T(n) = 4T(n/2) + (n) has solution T(n) = O(n²)

8. Solve the following recurrence relations. (16 points) a. T(n) = 4T(n-1) + 1 for n > 1; T(1) = 1; b. T(n) = T(n/2) + 3; T(1) = 1; Here you can assume that n=2k for some integer k.

Given the functions T( n) = n? + 3n and F( n ) = 2n², which of the following is the most accurate description of these two functions: O a. T(n) = O(F( n )) O b. T(n) = O(F( n )) O. T(n) = Q(F( n )) O d. None of them is correct

If lim n->oo (f(n))/(g(n)) = 0 then f(n) = ω( g(n) ) true false