## v.s 3 years ago Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim sqroot t+ t^2/6t − t^2 t→inf

1. TuringTest

$\lim_{t\to\infty}\frac{\sqrt{t+t^2}}{6t-t^2}$is this right?

2. v.s

the sqaure root is on for the t

3. TuringTest

$\lim_{t\to\infty}\frac{\sqrt t+t^2}{6t-t^2}$

4. v.s

yeyeyeey

5. TuringTest

divide top and bottom by t^2

6. v.s

$\frac{ \sqrt{t} }{ 6t }$

7. TuringTest

?

8. TuringTest

divide each term by t^2

9. v.s

i'm oo confused can you show me

10. TuringTest

$\lim_{t\to\infty}\frac{\frac1{t^2}(\sqrt t+t^2)}{\frac1{t^2}(6t-t^2)}$

11. TuringTest

distribute

12. v.s

whats is the answer

13. TuringTest

this site is about teaching, not handing out answers can you not simplify the numerator and denominator? this is algebra, you should know this.

14. v.s

sqroot(t)/t^2

15. v.s

6t;t^2

16. TuringTest

what about the t^2's on the right?

17. TuringTest

what is$\frac1{t^2}(\sqrt t+t^2)$?

18. v.s

doesn't the t^2/t^2 cancels out

19. TuringTest

cancels to what?

20. v.s

1

21. TuringTest

yes, but you never wrote the 1

22. v.s

ohhh

23. v.s

(sqroot (t)+1)/t^2/(6t-1)/t^2

24. TuringTest

those 1's should not be over t^2, they cancel like you said

25. TuringTest

just do the top$\frac1{t^2}(\sqrt t+t^2)$

26. v.s

okaay

27. v.s

sqroot (t)/t^2 +1/ 6t/t^2 +1

28. TuringTest

yes, and what is sqrt(t)/t^2 simplified?

29. v.s

i don"t know

30. TuringTest

$\sqrt[b]{x^a}=x^{a/b}$so$\sqrt t=t^{1/2}$and$\frac{t^a}{t^b}=t^{a-b}$use those two rules together

31. v.s

okaay thambi

32. v.s

3root (t^2)