Determine whether each of these functions = O(x^3 ) Justify your answer

f(x) = x^3 + 24.

f(x)=15x (x^2+1)

f(x)=11x log_2(x^11 )

f(x)= 4x!

f(x)=7^x

PROBLEM 4

Given the pseudocode, estimate its running time complexity in terms of Big-O (give tight bound).

a)

for ( i = 0; i < N; i++ ) { 

 for ( j = 0; j < N; j++ ) { 

 for ( k = 0; k < N; j++ ) { 

 statement;// printing stuff 

 } 

 } 

} 

b)

for ( i = 0; i < N; i++ ) { 

 for ( j = 0; j < N; j++ ) { 

 statement;// printing stuff 

 } 

} 

for ( k = 0; k < N; j++ ){ 

 statement;// printing stuff 

} 

c)

while ( low <= high ) { 

 mid = ( low + high ) / 2; 

 if ( target < list[mid] ) 

 high = mid - 1; 

 else if ( target > list[mid] ) 

 low = mid + 1; 

 else break; 

}