Question-60

Question-60

To establish a big-O relationship, find witnesses C and k such that

\left | f(x)\right |\leq C \left | f(x) \right | whenever x > k.

Find the least integer n such that f (x) is  O (x^{n})  for each of the functions.

a)  f(x) = 5x^{5} + x^{7}log x

n = ?

 

b)  f (x) = 4x^{7} + (log x)^{4}

n = ?

 

c)  f (x) =\frac{ x^{5} + x^{4} + 1 }{ x^{5} + 1 }

n = ?

 

d)  f (x) =  \frac{x^{5} +7 log x}{x^{6}+1}

n = ?

 

Solution

a) 8

b) 7

c) 0

d) -1

 

 

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