## appleduardo Group Title whats the limit of the following function? one year ago one year ago

1. appleduardo Group Title

$\frac{ x ^{2}-\sqrt{x} }{ 1-\sqrt{x} }$

2. appleduardo Group Title

x-->1

3. zordoloom Group Title

Do you know how to solve this?

4. shubhamsrg Group Title

you may try rationalizing, both numerator and denom separately..

5. appleduardo Group Title

but how can i do that? do first the denomitador and then de numerator or both at the same time?

6. shubhamsrg Group Title

doesnt matter..

7. shubhamsrg Group Title

any order you prefer..

8. appleduardo Group Title

??

9. zordoloom Group Title

The limit is -3.

10. shubhamsrg Group Title

you may rationalize either denom or nume first,,order wont matter..

11. sauravshakya Group Title

Use L'Hospital Rule

12. appleduardo Group Title

mm but how? maybe something like this? $\frac{ x ^{2} +\sqrt{x} }{ x ^{2} +\sqrt{x} }$ multiply the original function times the rationalization of the numerator?

13. godfreysown Group Title

i get 3x

14. appleduardo Group Title

yeep, i know the limit, but what i dont, is how to find it

15. zordoloom Group Title

Just take the derivative of the top, and then take the derivative of the bottom,

16. sauravshakya Group Title

It is -3

17. zordoloom Group Title

Then plug in 1 for x and that will give you the limit.

18. appleduardo Group Title

mm but how can i find the limit without using L'hopital? cos my teacher doesnt allow me to do that yet, he want me to find the limit algebraically

19. appleduardo Group Title

:/

20. zordoloom Group Title

Just multiply top and bottom by conjugates then.

21. appleduardo Group Title

respectively? i mean the numerator conjugate times the original numerator and the denominator conjugate times the original denominator?

22. zordoloom Group Title

no,

23. zordoloom Group Title

What you want to do is rationalize one side.

24. zordoloom Group Title

So, just multiply top and bottom by 1+sqrt(x)

25. zordoloom Group Title

You should get 1-x for the bottom

26. appleduardo Group Title

$\frac{ x ^{2}-\sqrt{x}(1+\sqrt{x}) }{1-x }$ so thts my result after doing what u said :p is it correct?

27. Aussie Group Title

you would have parenthesis around x^2 and sqrt x

28. appleduardo Group Title

mm yes so what can i do next?

29. Aussie Group Title

I am not sure actually you still have on the denominator 1-1 which is still dividing by a zero

30. Aussie Group Title

31. hartnn Group Title

$$\huge\frac{ (x ^{2}-\sqrt{x})(1+\sqrt{x}) }{1-x }\times \frac{x^2+\sqrt x}{x^2+\sqrt x}$$

32. hartnn Group Title

x^4-x = x(x^3-1) = x(x-1)(x^2x+x+1)

33. hartnn Group Title

put x=1 after cancelling 1-x