Christos 2 years ago Solve the limit limit(x-->+infinity) sqrt((x-3)/x)

1. satellite73

the square root grows slower so the limit will be zero

2. agent0smith

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

3. Christos

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

4. Christos

sqrt((x-3)/x)

5. satellite73

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

6. Christos

Yes thats correct

7. satellite73

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

8. satellite73

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

9. agent0smith

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

10. Christos

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

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

12. Christos

@satellite73

13. Christos

ohh let me try hold on

14. Christos

What do you mean by limit laws?

15. agent0smith

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

16. agent0smith
17. Christos

so thats infinity - infinity - infinity = +infinity?

18. agent0smith

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

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

20. agent0smith

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