How do you find the limit as x approaches positive infinity #((x^2)-2x+3)/(6-(3x^4))#?

1 Answer
Tessalsifi
Jun 2, 2015

We are going to seek the limits of the highest powers.

  • For the numerator :
    The highest power is #x²#
  • For the denominator :
    The highest power is #-3x^4#

The limit of your equation is thus #lim((x²)/(-3x^4))#
#=lim((-x²)/(3x²*x²))#

We simplify by #x²# :

#=lim((-1)/(3x²))#

And we know that #lim(3x²)# is #+prop#
And dividing -1 by a number approaching #+prop# makes it approch #0# ( staying negative )

Thus : #lim((x²-2x+3)/(6-(3x^4)))=0#

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