anonymous
  • anonymous
limit evaluation
Calculus1
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
\[\lim_{x \rightarrow -4}\frac{ \sqrt{x^9+9}-5 }{ x+4 }\]
myininaya
  • myininaya
Try rationalizing the top by multiply the numerator and denominator by the top's conjugate
anonymous
  • anonymous
I worked it out to \[\frac{ x^9-16 }{ x+4(\sqrt{x^9+9}+5) }\]

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anonymous
  • anonymous
I dont know what I would expand the top to
anonymous
  • anonymous
@myininaya
myininaya
  • myininaya
and i think you mean to have parenthesis around the (x+4) too on bottom
anonymous
  • anonymous
yes
myininaya
  • myininaya
try factoring the top to see if there is a factor of x+4 in it so you can get rid of what would make the bottom 0
anonymous
  • anonymous
I dont know how I would factor the top though and also with it being ^9 it's still a negative square root
myininaya
  • myininaya
do you know how do synthetic division or long division?
anonymous
  • anonymous
I should but I dont remember
myininaya
  • myininaya
ok well if you did know how and you determine there was no remainder then the limit does exist but if there is a remainder then the limit will not exist but i guess you can also determine this from just pluggin in -4 on both top and bottom if you have 0/0 the limit will exist if you don't then it won't
myininaya
  • myininaya
if the limit does exist then you of course must find it but if the limit doesn't exist, then you are done and dne is your answer
anonymous
  • anonymous
the limit does exist I know that, and I went back to my algebra 2 notes and doing synthetic division (x+4) is not a factor
myininaya
  • myininaya
how do you get the limit exists?
anonymous
  • anonymous
This is part of a review and when I put DNE, I was told I was incorrect
myininaya
  • myininaya
This question doesn't have a real limit had the function only exist for values where x^9+9 is greater than or equal to 0 anyhow x^9 has to be greater to 0 which means x cannot be negative because if it makes since to say if x is negative then x^9 is definitely more and most negative
myininaya
  • myininaya
sense not since*
myininaya
  • myininaya
you can even see a numerical approach will also show nothing exists to the left and right of -4 or at -4 (even though we aren't really concerned what happens at -4)
myininaya
  • myininaya
http://www.wolframalpha.com/input/?i=y%3D%28sqrt%28x%5E9%2B9%29-5%29%29%2F%28x%2B4%29+real of course there are some negative values the function does exist for after all x^9+9 has to be greater than or equal to 0
myininaya
  • myininaya
i misphrased it a little above when i just said x^9 has to be greater than or equal to 0 only small negative values will work anyhow is what i mean
myininaya
  • myininaya
as you can also tell from the graph nothing exists around x=-4
myininaya
  • myininaya
the limit does not exist we have determine this algebraically, graphically, and numerically
myininaya
  • myininaya
\[\lim_{x \rightarrow -4}\frac{\sqrt{x^9+9}-5}{x+4}\] just to be certain this was the problem right?
anonymous
  • anonymous
yes
myininaya
  • myininaya
so what is needed to convince you this limit does not exist? like which explanation does not make sense?
anonymous
  • anonymous
It's not that none of the explanations don't make sense. I came to the same conclusion working it myself. It's just that when I plugged in my answer what the test told me was that, that answer is incorrect
myininaya
  • myininaya
we can try to determine where the written went wrong in writing the test
myininaya
  • myininaya
give me a second and let me see if i can find out where they went wrong in writing the problem because i bet you that is what happened
myininaya
  • myininaya
writer* not written
anonymous
  • anonymous
could I ask you one other problem real quick first
myininaya
  • myininaya
so if they are saying the limit exist then that means they want some (x+4)'s to cancel... so one second
myininaya
  • myininaya
ok ask
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%281%2B%281%2F%28x%2B1%29%29%29 For the domain why is it x=/=2 and x=/=-1
anonymous
  • anonymous
-2*
anonymous
  • anonymous
I got the -2 but not why -1 also
myininaya
  • myininaya
do me a favor while i look at that try to answer that same question as if you were answering \[\lim_{x \rightarrow -4}\frac{\sqrt{x^2+9}-5}{x+4}\]
myininaya
  • myininaya
i think you might get it right if you pretend that is the question
anonymous
  • anonymous
alright
myininaya
  • myininaya
let me know and if you get it wrong i'm out of guesses of what they meant
myininaya
  • myininaya
ok you have a fraction inside that fraction
myininaya
  • myininaya
that one fraction does not exist at x=-1
myininaya
  • myininaya
and then after that of course you already knew to find when 1+1/(x+1) is not 0 which is when x=-2
myininaya
  • myininaya
for example when pluggin in -1 we get \[\frac{1}{1+\frac{1}{-1+1}}=\frac{1}{1+\frac{1}{0}} \] but 1/0 is not a number
anonymous
  • anonymous
alright so for \[\frac{ \sqrt{x^2+9}-5 }{ x+4 }\] I get\[\frac{ (x-4) }{ \sqrt{x^2+9}+5 }\] which still gives a negative root when I plug in -4
myininaya
  • myininaya
so 1/(1+1/0)) is still not a number
myininaya
  • myininaya
no it doesn't
anonymous
  • anonymous
sorry forgot ^2
anonymous
  • anonymous
so yeah never mind it gives 0
myininaya
  • myininaya
:(
myininaya
  • myininaya
ok you plugged in -4 right?
myininaya
  • myininaya
\[\frac{-4-4}{\sqrt{(-4)^2+9}+5}\] I think you are getting tired of this problem and you aren't going through the arithmetic slowly enough
myininaya
  • myininaya
-4-4 is -8
myininaya
  • myininaya
and can you do the bottom?
anonymous
  • anonymous
\[\sqrt{16+9}=\sqrt{25}....... 5+5=10\] so 8/10 or 4/5
myininaya
  • myininaya
don't forget the negative sign from the top
myininaya
  • myininaya
so -4/5 tell me if that is what they were looking for or not
anonymous
  • anonymous
I don't know because it doesn't show me the correct answer, but it is something
myininaya
  • myininaya
you should let your teacher know of the mistake though
myininaya
  • myininaya
most teachers (or some teachers) are amazed by students who can find there errors
myininaya
  • myininaya
their*
anonymous
  • anonymous
I haven't met them yet, and I don't head to school until another week. What would be the most respectable non-annoying way to present it?
myininaya
  • myininaya
Definitely don't rub in there face. I would just bring it up once if and when they respond. I think an email would be just fine. You can be like: Hey professor, As I was taking the exam, I came across the problem lim (x->-4) (sqrt(x^9+9)-5)/(x+4) and I said the limit does not exist but it was returned incorrect by the exam. I was thinking it was meant to be lim (x->-4) (sqrt(x^2+9)-5)/(x+4) where the answer would be -4/5. Please let me know if I'm correct or not. Sincerely, (you) But don't say she made a mistake. Just say the exam or whatever. What I'm saying is don't say YOU in the email. Try not to imply it is the teacher's fault even though it is. I think that is the best way.
myininaya
  • myininaya
Or dear professor if you are feeling more formal.
anonymous
  • anonymous
alright should I provide an explanation of my work about how I could not find the limit algebraically, graphically, or numerically for the original problem
myininaya
  • myininaya
I think you could say just nothing exists around -4 since x^9+9 has to be greater than or equal to 0. You know which means x^9>=-9 But for x values less than -4 certainly do not satisfy the inequality x^9>=-9. You could actually solve that inequality if you wanted to. x>=(-9)^(1/9) but values really close to -4 are definitely not in the set [(-9)^(1/9),inf)
anonymous
  • anonymous
alright thank you for all you help
myininaya
  • myininaya
Np. I don't have problem helping you with this one on your test mainly because it was written wrong. But I hope you intend to give the rest of the test your own knowledge.
myininaya
  • myininaya
Good luck @recon14193

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