Thread: Find the limit

Show that lim x--> infinity square root (x^2+x) -x = 1/2

note the x^2 + x is under the root only

Here's what I did so far:

[square root (x^2+x) -x] [square root (x^2+x) +x] / [square root (x^2+x) +x]

If we expand it out it becomes:

x^2+x + x[square root (x^2+x)] - x[square root (x^2+x)] - x^2 / [square root (x^2+x) +x]


1/ [square root (x^2+x) +x]

annnd that's where i lose it.. (if i ever had it from the start)

Originally Posted by alisheraz19

Show that lim x--> infinity square root (x^2+x) -x = 1/2

note the x^2 + x is under the root only

Here's what I did so far:

[square root (x^2+x) -x] [square root (x^2+x) +x] / [square root (x^2+x) +x]

If we expand it out it becomes:

x^2+x + x[square root (x^2+x)] - x[square root (x^2+x)] - x^2 / [square root (x^2+x) +x]


1/ [square root (x^2+x) +x]

annnd that's where i lose it.. (if i ever had it from the start)

The last expression is wrong: it must have x in the numerator. No wonder, since you expanded the product in the numerator in a terrible way: didn't you pay attention to the fact that you had an expression of the very easy form difference of squares?
Fix this, and then multiply the whole expression by so that you'll be able to divide each term in numerator and denominator by x (and get the x into the square root as ...!)

Tonio

I'm not quite following, the expression I have so far is :

x / square root (x^2+x) + x note* x^2+x is under the root only

i don't understand how to get 1/2 from here.. i expanded it out that way because i'm not very good with remembering rules ..

where do i go from here? how does multiplying by 1 = 1/x / 1/x ?

Originally Posted by alisheraz19

I'm not quite following, the expression I have so far is :

x / square root (x^2+x) + x note* x^2+x is under the root only

i don't understand how to get 1/2 from here.. i expanded it out that way because i'm not very good with remembering rules ..

where do i go from here? how does multiplying by 1 = 1/x / 1/x ?

Do you understand what to do from here?