Question

find the limit of sqrt[(x)(x+c)] - x
where c is a constant
as x approaches positive infinity

Answer 1

\[\lim_{x \rightarrow \infty}(\sqrt{x^2+xc}-x)\]
is this correct?

Answer 2

yes

Answer 3

looks like negative infinity

Answer 4

\[\lim_{x \rightarrow \infty}\frac{\sqrt{x^2+xc}-x}{1} \cdot \frac{\sqrt{x^2+xc}+x}{\sqrt{x^2+xc}+x}\]
Try multiply by top's conjugate on bottom and top like i have here

Answer 5

then look at the bottom to see what to divide top and bottom by

Answer 6

ok give me a minute to compute :)

Answer 7

i got -x^2/1 lol. my calc class is on extrema though no on infinite limits yet

Answer 8

so far I have \[\frac{ x^{2}+xc-x }{ \sqrt{x ^{2}+xc}+x} \]

Answer 9

x*x=x^2
\[\frac{ x^{2}+xc-x^2 }{ \sqrt{x ^{2}+xc}+x}\]

Answer 10

OH!

Answer 11

\[\lim_{x \rightarrow \infty} \frac{xc}{\sqrt{x^2+xc}+x}\]

Answer 12

so where should I go from here?

Answer 13

so you want to divide both top and bottom by the highest degree on bottom
but you have a sqrt on bottom so divide both top and bottom by sqrt(x^2)
and sqrt(x^2)=x if x>0
sqrt(x^2)=-x if x<0
we are approaching positive infinity so we are looking at using sqrt(x^2)=x