21. Let f(n) = n² + 20 and g(n) = n³. (a) Show that f(n) is O(g(n)) by finding a positive integer A for which f(n) < A g(n) for all n ≥ 1. (b) Show that f(n) is O(g(n)) by finding a positive integer N for which f(n) < g(n) for all n > N. (c) Use proof by contradiction to show that g(n) is not O(f(n)).

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A: Topic: differentiation

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A: Ans:  for     n≥2 f(n)(1) does not exists.

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A: Solution:Given   f(x)=4-x+x-4To find the domain of f(x)

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Q: #8: Suppose that an = as 8n a₁²2² +2a₂x³ + 3a3x²4 + 4a4x³ + ... (i) Σf(n)x"+2 n=0 (ii) g(n)x+1 We…

A: This is a good exercise in summation and we shall see how to change the indices.

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: This is an example of composition of function. Put the function g in f intended of x for fog(x)

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