Consider the function f(n) = 18n 2 − 2n 2 log (n) + 5n 3 which represents the complexity of some algorithm. (a) Find the smallest nonnegative integer p for which n p is a tight big-O bound on f(n). Be sure to justify any inequalities you use and provide the C and k from the big-O definition. (b) Find the largest nonnegative integer p for which n p is a tight big-Ω bound on f(n). Be sure to justify any inequalities you use and provide the C and k from the definition. (c) Based on your work in parts (a) and (b), what is the order of f? (d) Verify that your answer in part (c) is correct by computing any relevant limits. Show all work.

Step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

10/60

step-by-step explanation:

if you divide 10 by 60 the answer is 0.166666 while if you divide or solve the other problems it equals 0.6