## Christos Group Title Solve the limit limit(x-->+infinity) sqrt((x-3)/x) one year ago one year ago

1. satellite73 Group Title

the square root grows slower so the limit will be zero

2. agent0smith Group Title

Divide both numerator and denominator by x, to solve it algebraically.

3. Christos Group Title

I am sorry the actual epression is sort(x-3/x)

4. Christos Group Title

sqrt((x-3)/x)

5. satellite73 Group Title

$\lim_{x\to \infty}\sqrt{\frac{x-3}{x}}$?

6. Christos Group Title

Yes thats correct

7. satellite73 Group Title

then it is one since $$x-3$$ and $$x$$ grow at the same rate

8. satellite73 Group Title

think what it would be like if $$x$$ was $$1,000$$ you would have $\sqrt{.993}$

9. agent0smith Group Title

$\Large \lim_{x\to \infty}\sqrt{\frac{x-3}{x}} = \sqrt {\lim_{x\to \infty}\frac{x-3} {x}}$

10. Christos Group Title

bro I am trying to solve this limit actually http://screencast.com/t/Yoo5IO0bRPjD And I ended up in the expression above, but what you give me isnt the final answer, something must be wrong :(

11. agent0smith Group Title

@Christos that's a completely different expression... break it up using limit laws.

12. Christos Group Title

@satellite73

13. Christos Group Title

ohh let me try hold on

14. Christos Group Title

What do you mean by limit laws?

15. agent0smith Group Title

$\Large = \lim_{x \rightarrow \infty} \sqrt{x^2 - 3x} -\lim_{x \rightarrow \infty} x$

16. agent0smith Group Title
17. Christos Group Title

so thats infinity - infinity - infinity = +infinity?

18. agent0smith Group Title

From a graph it looks like it'll be -1.5, I'm just trying to find a way to show that algebraically.

19. Christos Group Title

It's ok man dont brother I found it thank you

20. agent0smith Group Title

Yeah i'm glad i didn't try to do it myself... wolfram gives a looooong solution: http://www3.wolframalpha.com/Calculate/MSP/MSP35891gdgbb0f2cc1ecie00005387i303c364idgg?MSPStoreType=image/png&s=42&w=433&h=1816