Find the limit or show that it does exist, lim goes to infinity of (sqrt 1+4x^6)/(2-x^3)

Question

Please help 

Answer 1

   L  =   √(1 + 4 x⁶)   /(2 - x³)      can be rearranged by pulling a factor of x³ out of the numerator and denominator.

 

    These factors of x³ cancel leaving

 

    L  =   √(4 +  1/x⁶ ) / (2/x³ -1)  

 

   In this form, the limit as x →∞   is straightforward because the limit x →∞ of both 1/x³  and 1/x⁶  = 0

 

   So   lim x→∞  L  =    √4/(-1)   =  -2