SOLUTION: I need to find the slant asymptotes of
a. x^3+x^2/x^2-4
b. 2x^2+10x-12/x^2+x-6
I understand how to find the Vertical and Horizontal, but I'm confused on the slant portion.
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Question 734948: I need to find the slant asymptotes of
a. x^3+x^2/x^2-4
b. 2x^2+10x-12/x^2+x-6
I understand how to find the Vertical and Horizontal, but I'm confused on the slant portion. Please help! thank you!!!
Found 2 solutions by lynnlo, MathLover1:
Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
to find the slant asymptotes of
a.
The vertical asymptotes (and any restrictions on the domain) come from the zeroes of the denominator, so I'll set the denominator equal to zero and solve.
if ...=>...
if ...=>...
Then the domain is all other than ± , and the two vertical asymptotes are at
and .
Since the degree is greater in the denominator than in the numerator, the will be dragged down to the , and the horizontal asymptote is therefore "" (the ) .
The slant asymptote: use the long division to find it
----------
--------|
)..
_________________
----------
------------
________________
---------------
---------------
so, since is a factor of the numerator
the slant asymptote:
b.
horizontal asymptote: -> to as -> or
so,horizontal asymptote is
continue factoring
find values that make denominator equal to zero:
if....->...
if....->...
these are vertical asymptotes
-there is no slant asymptote in this case
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