## Jusaquikie 3 years ago lim 8e^(TanX) x → (π/2)+

1. Jusaquikie

not sure where to go to with this

2. TuringTest

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

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

4. TuringTest

?

5. Jusaquikie

+infinity?

6. Jusaquikie

.027

7. TuringTest

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

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

9. Jusaquikie

tan(pi/2) lol

10. TuringTest

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

11. Jusaquikie

yes

12. TuringTest

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

13. Jusaquikie

1/0= undefined

14. TuringTest

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

cosine*

16. Jusaquikie

positive and increasing to 1?

17. TuringTest

no, what is the cosine of pi/2 ?

18. Jusaquikie

0 sorry was thinking sin

19. Jusaquikie

so negative

20. TuringTest

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

0

22. TuringTest

no, think in terms of sin and cos

23. Jusaquikie

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

24. Jusaquikie

2pi

25. TuringTest

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

what is sine approaching? what is cos approaching?

27. Jusaquikie

1,0

28. TuringTest

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

29. Jusaquikie

negative?

30. TuringTest

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

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

-infinity?

33. Jusaquikie

no + infinity

34. TuringTest

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

35. TuringTest

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

36. TuringTest

$\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

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

38. Jusaquikie

ok

39. TuringTest

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

40. Jusaquikie

zero?

41. TuringTest

correct :)

42. Jusaquikie

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

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

44. Jusaquikie

yes thanks