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) = 4 $x^{7} + (log x)^{4}$

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