## Jusaquikie Group Title lim 8e^(TanX) x → (π/2)+ one year ago one year ago

1. Jusaquikie Group Title

not sure where to go to with this

2. TuringTest Group Title

since$\Large\lim_{x\to a}e^{f(x)}=e^{\lim_{x\to a}f(x)}$really all you need to know is the limit$\Large\lim_{x\to\pi/2^+}\tan x$

3. TuringTest Group Title

what is$\lim_{x\to\pi/2}\tan x$

4. TuringTest Group Title

?

5. Jusaquikie Group Title

+infinity?

6. Jusaquikie Group Title

.027

7. TuringTest Group Title

actually it depends on the left and right hand approach from the left (x<pi/2) cos x>0 from the right (x>pi/2) cos x<0

8. TuringTest Group Title

I have no idea where you got that number from....

9. Jusaquikie Group Title

tan(pi/2) lol

10. TuringTest Group Title

I'm gonna take a wild guess and say you left your calculator in degree mode

11. Jusaquikie Group Title

yes

12. TuringTest Group Title

$\tan x=\frac{\sin x}{\cos x}$so$\tan (\pi/2)=\frac{\sin (\pi/2)}{\cos (\pi/2)}=?$

13. Jusaquikie Group Title

1/0= undefined

14. TuringTest Group Title

right, now what about coming from the right, x>pi/2 will cosince be positive or negative approaching pi/2 from the right?

15. TuringTest Group Title

cosine*

16. Jusaquikie Group Title

positive and increasing to 1?

17. TuringTest Group Title

no, what is the cosine of pi/2 ?

18. Jusaquikie Group Title

0 sorry was thinking sin

19. Jusaquikie Group Title

so negative

20. TuringTest Group Title

correct, so as $$x\to\pi/2^+$$ we have that $$\cos x\to0$$, which means that$\lim_{x\to\pi/2^+}\tan x=?$

21. Jusaquikie Group Title

0

22. TuringTest Group Title

no, think in terms of sin and cos

23. Jusaquikie Group Title

anything with Euler's number just confuses me, i'm not sure how to treat it

24. Jusaquikie Group Title

2pi

25. TuringTest Group Title

ignore Euler's number, it could be any exponential base, the answer would be the same...$\lim_{x\to\pi/2^+}\frac{\sin x}{\cos x}=?$what is sine approaching? what is cos approaching?

26. TuringTest Group Title

what is sine approaching? what is cos approaching?

27. Jusaquikie Group Title

1,0

28. TuringTest Group Title

and is that zero being approached from the negative or positive side?

29. Jusaquikie Group Title

negative?

30. TuringTest Group Title

correct, so considering that$\lim_{x\to\pi/2^+}\tan x=\lim_{x\to\pi/2^+}\frac{\sin x}{\cos x}\to\frac10$and that that zero is being approached from the negative side, what is the limit?

31. Jusaquikie Group Title

i can't visualize it and i'm not sure how to graph it in my calculator so i'm trying to relate it to the unit circle

32. Jusaquikie Group Title

-infinity?

33. Jusaquikie Group Title

no + infinity

34. TuringTest Group Title

|dw:1347837808350:dw|you were right the first time, -infty

35. TuringTest Group Title

positive number (sine) being divided by a small negative number (cosine) is a large negative number

36. TuringTest Group Title

$\frac1{-0.1}=-10$$\frac1{-0.01}=-100$$\frac1{-0.001}=-1000$etc., so as cos x goes to zero from x>pi/2 we approach $$-\infty$$

37. TuringTest Group Title

hence$\lim_{x\to\pi/2^+}\tan x=-\infty$

38. Jusaquikie Group Title

ok

39. TuringTest Group Title

so then what is$\lim_{x\to\pi/2^+}8e^{\tan x}$

40. Jusaquikie Group Title

zero?

41. TuringTest Group Title

correct :)

42. Jusaquikie Group Title

thanks for the long journey, i'm just really tired and burnt out right now, sorry you had to work so hard on this one

43. TuringTest Group Title

it's fine, much better than just pumping out an answer you won't comprehend hopefully you learned something is the idea ;)

44. Jusaquikie Group Title

yes thanks