1. Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic d
ID: 3586264 • Letter: 1
Question
1. Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic definition of notation, prove that max (fin), g(n)) = (f(n) + g(n)) 2. Prove that o(g(n)) n a(g(n) is the empty set.. Q3. Identify the class of function to which t(n)-3n3+20n2+5 belongs. Show your detailed analysis of how you arrived at your conclusion. Q4. In each of the following situations, indicate whether f = 0(g), or f-Mg), or both (in which case f= (g) (a) f(n) = 100n + log n g(n) = n + (log n)2 (b) f(n) = 10 log n (c) fin) = n2/log n g(n) = n(log n)' (d) f(n) = (log n)log n g(n) = 2(log2 n (e) f(n) = 1 1 k g(n) = log(n2) g(n) = nk+1Explanation / Answer
Answer:
3. t(n) = 3n^3 + 20n^2 + 5
This belongs to a cubic function. Let we see how ?
The cubic capacity f(n) = n^3. This capacity seems less habitually with regards to the calculation examination than the steady, direct, and quadratic capacities. It's down to earth for utilize just on little issues. At whatever point n pairs, the running time increments eightfold.
Illustration: n by n grid increase.
The capacities we have adapted so far can be seen as all being a piece of a bigger class of capacities, the polynomials. A polynomial capacity is a component of the frame:
anx^n + a 1 +x^n-1 +...+a2x^2+a1x + a0
where a0, a1, ... , an are constants, called the coefficients of the polynomial, and a != 0. Whole number n, which shows the most noteworthy power in the polynomial, is known as the level of the polynomial.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.