1. A.,. Give a Big-O estimate that is as good as possible for each of the following functions. (n³ + n)(logn+ n) ii. (n + 1000)(logn + 1) i. If these are complexities of algorithms that solve the same problem, which one would you prefer? Why? В. C. Considering the Big-O complexity, how many times is your choice faster with respect to the other solution for an input size of 216? Note: The base of logarithm is 2.
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- Considering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point iteration. Assume an initial guess of 1. Use the equation form that will seem fit according to the choices provided.Group of answer choices 0.72210 0.71537 0.76396 0.72236Find the relation between the following functions: f(n) = log n and g(n) = Vn. (Square root for n)Hint: you may use L'Hopital's Theorem. For function f(n)=log n and time t=1 second, determine the largest size n of a problem that can be solved in time t, assume that the algorithm to solve the problem takes f(n) microseconds. Suppose you have algorithms with the two running times listed below. Suppose you have a computer that can perform 6 operations per second, and you need to compute a result in at most an hour of computation. For each of the algorithms, what is the largest input size n for which you would be able toget the result within an hour for:a) n^3b)10n^2Let f (f(n) and g(n)) be asymptotically nonnegative functions. Using the basic definition of Θ notation, prove that max(f(n), g(n)) = Θ(f(n) + g(n)),
- You are given a third-degree polynomial function f(x) as follows. f(x)=x3-43x+42 x0=2.4, x1=1, x2=3, n=90 Note that the answers are given with exactly 3 digits after the decimal point. Could you write the codes by using Pyhton 3 according to the questions in the picture which I uploded?In R-Studio Problem 2. Find a large set of integers (with at least 10000 observations) representing a sample drawn from real life (i.e., do not generate the numbers using some random number generator). First, explain what the integers correspond to in real life. Then, investigate the distribution of the integers, and also the first and last digits of the integers in this sample (For example, if the data has [34 65], plot the distribution of these numbers and also distribution of [3,6] and [4 ,5] separately). Does any of these digits follow a uniform distribution? Is this expected? If one of them does not follow a uniform distribution, what distribution does it follow? Can you explain why? [You can analyze the image age dataset provided by IMDB Wiki, which contains the ages of actors and actresses whose photos are present in the IMDB database. The data contains 459868 age values in years, ranging from 1 to 99 years.]#Use python to solve this math #Find the minima and maxima of the following functions at a given interval 1. y= 9x 3 −7x 2 +3x+10 in the interval [-5, 6] 2. y= ln x [-5, 6] 3. y= sin x [-5, 6] 4. y= cos x [-5, 6] 5. y= tan x [-5, 6]
- 1. Prove the following formulas log X < X for all X > 0You are given a third-degree polynomial function ?(?) as follows. ?(?) = ?3 − 43? + 42 ?0 = 2.4, ?1 = 1, ?2 = 3, ? = 90 Could you write the codes by using Pyhton 3 according to the questions in the picture which I uploded?Use the master theorem to determine the run-time complexity of the following function. Clearly indicate the values of a, b, and c that you are using.
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