How do you evaluate the limit #(x^2+4x+6)/(3x^2+1)# as x approaches #oo#?

1 Answer
Roy E.
Dec 5, 2016

#1/3#. Just ignore all the terms except the highest power top and bottom.

Explanation:

If the function is the quotient of two polynomials #{P(x)}/{Q(x)}# where the degree of #P# is the same as that of #Q# the limit will always be the ratio of the coefficients of the highest power. If the degree of #Q# is higher than that of #P# the limit will be zero; if the degree of #Q# is lower that that of #P# there will be no limit. Informally, as #x# gets larger and larger all the non-first terms of #P# and #Q# become negligible compared to the first.

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