limit involving infinity

[ladyfire]

find the value of the limit:

Lim (the square root of (x^2 +x)) -x
x--> infinity

can you explain this in steps. i am confused.

 

[stapel]

Try these steps:

1) Think of the given limit expression as being a fraction over "1". Multiply top and bottom by the conjugate of the numerator; namely, by sqrt[x² + x] + x. Simplify.

2) Divide top and bottom by x. Simplify, keeping in mind that dividing the square root by x (outside the root) is the same as dividing the argument of the root by x².

3) Take the limit of the remaining (much nicer) expression as x tends toward infinity.

Eliz.

 

[ladyfire]

ok. i had gotten as far as your step 2 before this post. but i don't know how everything should look after dividing by x.

 

[ladyfire]

did you get 1/ (the square root of (3) +1) ?

i got that from

(x/x) / [((the square root of (x^2 + x) +x))/x]

 

[Gene]

(x/x) / [((the square root of (x^2 + x) +x))/x]
should become
(x/x)/(sqrt((x^2+x)/x^2)+x/x =
1/(sqrt(1+1/x)+1)
Then take the limit