Find the least integer

n

such that

f(x)

is

O(x^(n))

for each of\ these functions.\ a)

f(x)=2x^(3)+x^(2)logx

\ b)

f(x)=3x^(3)+(logx)^(4)

\ c)

f(x)=(x^(4)+x^(2)+1)/(x^(3)+1)

\ d)

f(x)=(x^(4)+5logx)/(x^(4)+1)

Find the least integer

n

such that

f(x)

is

O(x^(n))

for each of\ these functions.\ a)

f(x)=2x^(3)+x^(2)logx

\ b)

f(x)=3x^(3)+(logx)^(4)

\ c)

f(x)=(x^(4)+x^(2)+1)/(x^(3)+1)

\ d)

f(x)=(x^(4)+5logx)/(x^(4)+1)

7. Find the least integer n such that f(x) is O(xn) for each of these functions. a) f(x)=2x3+x2logx b) f(x)=3x3+(logx)4 c) f(x)=(x4+x2+1)/(x3+1) d) f(x)=(x4+5logx)/(x4+1)