Question

lim x -> infinity (sqrt(x^2+5x) -x) L'hopital Explain Please

Answer 1

put x=1/y
then y->0
then you can apply L'Hopitals.

Answer 2

@hartnn isnt it somewhat the same question we answered yesterday

Answer 3

maybe, i don't remember.....

Answer 4

\[\lim_{x \rightarrow \infty}\sqrt{x^{2}+5x}-x\]
An indeterminate form
∞-∞
There might be a "more proper" way to do this, but here's my hunch:
Express it as \[\lim_{x \rightarrow \infty}\sqrt{x^{2}\left( 1-\frac{5}{x} \right)}-x\]and then
\[\lim_{x \rightarrow \infty}x \sqrt{ 1-\frac{5}{x}}-x\]NOTE that it's normally |x| outside the radical and not just x, but seeing as x is going to positive infinity anyway...\[\lim_{x \rightarrow \infty}x \left( \sqrt{ 1-\frac{5}{x}}-1 \right)\]So now, it's an indeterminate of the form
0· ∞
From which the use of L'Hôpital's rule can be more clearly seen :D

Answer 5

multiply by the conjugate, then it will be easier

Answer 6

you get
\[\frac{5x}{\sqrt{x^2+5x}+x}\] now you don't need l'hopital, your eyeballs will do

Answer 7

\(\frac{5x}{2x}=\frac{5}{2}\)

Answer 8

i think this one is just 5...hmm:
when you multiply by the conjugate wouldn't it be
√(x^2 +5x) multiply by conjugate (√(x^2+5x) +x) both numerator and denominator
x^2-√(x^2+5x) / x+ √(x^2 +5x)
then you simplify and you get
5x/ (x+√(x^2+5x)
Find the derivative
5/(1+1/2 (x^2+5x)^-1/2 (2x+5)
5/1+[(2x+5)/2√((x^2)+5x)

Answer 9

also, (2x+5)/2√((x^2)+5x) all of this is equal to 1

so, based on that ...lol i think i just proved myself wrong.
I multiplied the 1's in the denominator instead of adding
Yes, its 5/2
5/(1+1) =5/2

Answer 10

what happened to the -x at the end of the original equation karisos

Answer 11

I placed it in front of it but forgot to carry the negative sign so just leave it in the back. Bringing it upfront will just make things worse. I think the sign might make the answer negative. I'm pretty sure its 5/2 but i'm not completely sure if its -5/2. Since I forgot to carry the negative out it probably is -5/2. :/

Answer 12

the negative would make the 1on the denominator negative making both ones cancel out. So in the end, I'm back to the beginning now it looks like its just 5. I'm probably confusing u more. Sorry man

Answer 13

Here, I went on google and found this. Same question apparently...the answer there was 5/2

http://answers.yahoo.com/question/index?qid=20081102155643AA6WX8Z