## anonymous 3 years ago limit

1. anonymous

$\lim_{x \rightarrow -1} \sqrt{\frac{ 1-t^2 }{ 1+t }}$

2. anonymous

why is your limit has x approahing -1 and the function is in terms of t?

3. anonymous

that was a typo an my behalf :\$

4. anonymous

factor the numerator to (1+t)(1-t) then cancel the (1+t) out so you are left with $\sqrt{1-t}$

5. anonymous

then you can substitue

6. anonymous

@kphilips2010 that method is not correct

7. anonymous

i dont think i ca use conjugates for this question

8. anonymous

why is that wrong?

9. anonymous

because it's not a binomia

10. anonymous

binomial*

11. anonymous

12. anonymous

I didnt say it was a binomial, I am saying you can factor the binomial into (1+t)(1-t)

13. anonymous

but isnt there another method, like multiply by the denominator or something of the like

14. anonymous

no not in this case

15. anonymous

LOL i am sure I am right...I hope

16. anonymous

kphilips method is good imo.

17. anonymous

thanks joemath314159

18. anonymous

i know thats how i approached the question at first but my teacher said this method was wrong ? :S

19. anonymous

hmmm I feel dumb

20. anonymous

why did your teacher say you were wrong?

21. anonymous

i dont know she said there was something wrong with the method :S

22. anonymous

does she know what she is talking about? LOL

23. anonymous

sorry but i dont have another solution

24. anonymous

is this what you're saying |dw:1350442853605:dw|

25. anonymous

so do i keep the square root sign ?

26. anonymous

If you want to be rigorous about it, you need to state that for limits, you are looking at values of t close to -1, but NOT EQUAL to -1. if t is not equal to -1, then:$\frac{1-t^2}{1+t}=\frac{(1-t)(1+t)}{(1+t)}=1-t$We can only divide those monomials out if t DOESNT equal -1, which is ok in limits, we dont want t to equal -1. Im making an emphasis on the fact that if t was equal to -1, then that division doesnt make any sense.

27. anonymous

ohh i see what you're saying

28. anonymous

does the squareroot say there tho ?

29. anonymous

yes.

30. anonymous

yes the sq rt stay

31. anonymous

yay i was right.

32. anonymous

thanks :D