Question

By using L'Hopital Rule, the question is given....

Answer 1

\[\lim_{x \rightarrow \infty} (x -\sqrt{x ^{2}+x)}\]

Answer 2

I never studied L'hospital's rule. sorry.

Answer 3

saifoo in which grade u r now?

Answer 4

@saifoo.khan , its okay, thanks though :)

Answer 5

Rationalize it by\[x + \sqrt{x^2 + x}\]That is, divide and multiply by this and simplify. You will get:\[\frac{-x}{\sqrt{x^2 +x} + x}\]I think this is the way to go, try to simplify this by dividing by x.

Answer 6

okay @bmp did u get the answer -1/2

Answer 7

Yeah, doing the algebra, that seems to go to -1/2

Answer 8

I didn't see that, @bmp , nice job.

Answer 9

I got another idea, let me try it.

Answer 10

@bmp can u show the working?

Answer 11

Let me try mathematica evaulation.

Answer 12

It is -1/2

Answer 13

@fatinatikah , with what @bmp told you, do this.