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\[\lim_{x \rightarrow -4}\frac{ \sqrt{x^9+9}-5 }{ x+4 }\]

Try rationalizing the top by multiply the numerator and denominator by the top's conjugate

I worked it out to \[\frac{ x^9-16 }{ x+4(\sqrt{x^9+9}+5) }\]

I dont know what I would expand the top to

and i think you mean to have parenthesis around the (x+4) too on bottom

yes

do you know how do synthetic division or long division?

I should but I dont remember

how do you get the limit exists?

This is part of a review and when I put DNE, I was told I was incorrect

sense not since*

as you can also tell from the graph nothing exists around x=-4

the limit does not exist
we have determine this algebraically, graphically, and numerically

\[\lim_{x \rightarrow -4}\frac{\sqrt{x^9+9}-5}{x+4}\]
just to be certain this was the problem right?

yes

we can try to determine where the written went wrong in writing the test

writer* not written

could I ask you one other problem real quick first

ok ask

-2*

I got the -2 but not why -1 also

i think you might get it right if you pretend that is the question

alright

let me know
and if you get it wrong i'm out of guesses of what they meant

ok you have a fraction inside that fraction

that one fraction does not exist at x=-1

and then after that of course you already knew to find when 1+1/(x+1) is not 0
which is when x=-2

so 1/(1+1/0)) is still not a number

no it doesn't

sorry forgot ^2

so yeah never mind it gives 0

:(

ok you plugged in -4 right?

-4-4 is -8

and can you do the bottom?

\[\sqrt{16+9}=\sqrt{25}....... 5+5=10\] so 8/10 or 4/5

don't forget the negative sign from the top

so -4/5
tell me if that is what they were looking for or not

I don't know because it doesn't show me the correct answer, but it is something

you should let your teacher know of the mistake though

most teachers (or some teachers) are amazed by students who can find there errors

their*

Or dear professor if you are feeling more formal.

alright thank you for all you help

Good luck @recon14193