Find the limit if it exists It does lim xINFINITY X4 4X2 X

Find the limit, if it exists. (It does.)

lim x->INFINITY (X^4 - 4X^2 +X) /(X^3 - X +9)

I divided everything by X^4 but I\'m not sure if the limits for let\'s say -4x^2/x^4 =0

I thought the answer might be 1 (which means I assumed all other values divided by X^4 were 0 ... which was not the case.)

Solution

lim x->INFINITY (X^4 - 4X^2 +X) /(X^3 - X +9)

since degree of numerator is greaterthan denominaotr

limit tends towards infinity.