Find the horizontal limit(s) of the following function:
f(x) = \frac {11 x^3 - 9 x^2 -10 x }{ 9 - 11 x - 10 x^3 }
?and ?

- anonymous

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- anonymous

(-11x^3+9x^2+10x)

- anonymous

how so i solve it?

- Shayaan_Mustafa

kindly make standard form of your question. so I could understand.

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## More answers

- Shayaan_Mustafa

@rukh

- anonymous

Find the horizontal limit(s) of the following function:
f(x) = \frac {11 x^3 - 9 x^2 -10 x }{ 9 - 11 x - 10 x^3 }

- Shayaan_Mustafa

I told in fraction form correctly..

- Shayaan_Mustafa

\[f(x)=(11x ^{3}-9x ^{2}-10x)/(9-11x-10x ^{3})\]is this your fraction looks like?

- anonymous

see attached

##### 1 Attachment

- anonymous

yes

- Shayaan_Mustafa

ok now.. as in your question. horizontal limits mean domain of the function.
DOMAIN:
it is where function is defined.
for example
if\[\lim_{x \rightarrow 0}1/x=\infty\]
because anything divided by zero, goes to infinity. so the function is not defined at infinity. so every number except this is its domain. because at 0 1/x is not defined.

- Shayaan_Mustafa

got it ?

- anonymous

sort of

- anonymous

but the answer will be a set then?

- Shayaan_Mustafa

yes. it will be a set.

- anonymous

horizontal asymptote is the ratio of the leading coefficents, since the degree of the numerator and denominator are the same (they are both 3)

- Shayaan_Mustafa

\[f(x)=(11x ^{3}-9x ^{2}-10x)/(9-11x-10^{3})\]In this function denominator must not be zero.

- anonymous

therefore your horizontal asymptote is
\[y=-\frac{11}{10}\]

- anonymous

ok, my homework program does not accept a set as the answer, it says that the answers must be a number

- anonymous

and secondly - 11/10 is not being accepted either

- anonymous

then there is a mistake, but i can assure you that is what it is
unless they want you to write
\[y=-\frac{11}{10}\]

- anonymous

im supposed to get 2 answers for this problem

- anonymous

if -11/10 is one..whats the other?

- Mertsj

Did you double check to see if the problem is posted correctly?

- Mertsj

Or maybe they want it in decimal form.

- anonymous

yes its correct

- Mertsj

What's correct?

- Shayaan_Mustafa

it will define for all real numbers. X=all

- anonymous

the problem was posted correctly

- anonymous

i need 2 answers . if -11/ 10 is one, whats the other?

- Mertsj

I don't know. Are they asking for the horizontal asymptotes? Because there is only one.

- anonymous

there is one, it is the ratio of the leading coefficients. there is no other

- anonymous

this is so complicated....:(

- Mertsj

Maybe they want you to say as x approaches positive infinity, the limit is -11/10 and as x approaches negative infinity, the limit is -11/10

- anonymous

they are asking for horizonal limits...is this the same as horizontal asymptotes?

- Mertsj

Satellite???

- anonymous

ok both answers are -11/10 and they did want it in decimal form. thanks guys

- Mertsj

yw. I'll take the bows for Satellite's work.

- Shayaan_Mustafa

as I have solved this equation
vertical asymptote= NO
horizontal asymptote= -11/10
oblique asymptote= NO

- anonymous

\[f(x) = \frac {11 x^3 - 9 x^2 -10 x }{ 9 - 11 x - 10 x^3 }\] is what is written, i cannot read the word document.
numerator is a polynomial of degree 3
denominator is a polynomial of degree 3 (same degree)
horizontal asymptote, limit as x goes to infinity, etc is
\[y=-\frac{11}{10}=-1.1\] the ratio of the leading coefficeints. there is no other answer

- anonymous

thanks so much

- Shayaan_Mustafa

you are ever welcome.

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