## appleduardo 3 years ago whats the limit of the following function? could somebody help me pleasE?

1. appleduardo

$\frac{ \sqrt{2-t}-\sqrt{2} }{ t }$

2. appleduardo

t-->0

3. anonymous

first you want to multiply the top and bottom by the reciprocal of the top

4. anonymous

$\sqrt{2-t}+\sqrt{2}$

5. anonymous

multiply top and bottom by that, and what do you get?

6. appleduardo

yeep, but then i'll get this: $\frac{ 2-t-2 }{ t(\sqrt{2-t})+\sqrt{2}}$

7. anonymous

right.

8. anonymous

now simplify the top

9. appleduardo

ill get:$\frac{ -t }{ t(\sqrt{2-t} +\sqrt{2}) }$

10. anonymous

also, the denominator should be $t(\sqrt{2-t}+\sqrt{2})$

11. anonymous

correct. now can you do anything with the top and bottom t's?

12. appleduardo

is it right to cancel a negative t with a positive t ?

13. anonymous

well, you just cancel the t's, the negative would stay.

14. anonymous

so you would get $\frac{ -1 }{ \sqrt{2-t}+\sqrt{2} }$

15. anonymous

now you can take the limit directly by plugging in 0.

16. appleduardo

:O so the limit is: -0.353509207 ?

17. anonymous

well, I suppose if you want to do it that way, I would just say $\frac{ -1 }{ 2\sqrt{2} }$

18. appleduardo

oh God youre a genius! thank you so much!!!

19. anonymous

:) no worries.