determine whether the following pair of functions are in sam

determine whether the following pair of functions are in same order x^2 + x^3 +1 and 2x^2 i.e big theta

Solution

In Big-theta : we ignore all lower order terms and constant multipliers

x^2 + x^3 +1
   x^3 > x^2 > 1

   So Big-Theta: x^3

2x^2 :
   ignoring 2
   Big-Theta: x^2

So, both are not of same order