Question

How do in find the end behavior of these? lim f(x)
f(x)=6x^4-7x^2-10
f(x)=-x^3-5x^2+7x-10

Answer 1

take the limit at infinity

Answer 2

you need to find
\[\lim_{x \rightarrow \infty}6x^4-7x^2-10 \\ \lim_{x \rightarrow \infty}-3x^3-5x^2+7x-10\]

Answer 3

wouldnt thte first one just be (infinity,infinity)?

Answer 4

I haven't done this using limits, no use. Won't interfere more than what I did already though.

Answer 5

yes the first is oo that's the end behavior of the first at oo
the second is -oo

Answer 6

but this is usually an alg. question.
Oh oops, sorry xD

Answer 7

well this just a polynomial so no big deal, we pretty much know that i gives such end behaviors

Answer 8

it*

Answer 9

If we have polynomial functions, as we clearly do, then consider this:

-if it's an even degree polynomial with a positive leading coefficient then\[\lim_{x \rightarrow -\infty}f(x) =+\infty \]and\[\lim_{x \rightarrow +\infty}f(x) =+\infty \]-if it's an even degree polynomial with a negative leading coefficient, then\[\lim_{x \rightarrow -\infty}f(x)=-\infty \]and\[\lim_{x \rightarrow +\infty}f(x)=-\infty \]-if it's an odd degree polynomial with a positive leading coefficient, then\[\lim_{x \rightarrow -\infty}f(x)=+\infty \]and\[\lim_{x \rightarrow +\infty}f(x)=- \infty \]-ifit's an odd degree polynomial with a negative leading coefficient, then\[\lim_{x \rightarrow -\infty}f(x)=-\infty \]and\[\lim_{x \rightarrow +\infty}f(x)=+\infty \]

Answer 10

@xapproachesinfinity so the first one is \[(\infty,\infty) and the second one (-\infty,-\infty)?\]

Answer 11

no just infinity my friend
they are not asking for domain
lim f(x)=oo for the first one
refer to @calculusfunctions replay to see why is that true
the same for the second

Answer 12

oh ok I understand, but for the one with the x^3 would it just be infinity? since its x^3

Answer 13

correction
when the degree is odd and the coefficient is negative
\[\lim_{x \rightarrow \infty} f(x)=-\infty\]

Answer 14

i would be infinity but there is a negative coefficient attached to it
-x^3 which makes -infinity

Answer 15

it would*

Answer 16

Correction: in my notes above, for the last two examples, the conditions for a odd degree polynomial with a positive leading coefficient are at the bottom and the conditions for the odd degree with a negative leading coefficient are directly above the bottom. Sorry for the error.

Answer 17

thanks! i got it