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Jusaquikie Group Title

lim 8e^(TanX) x → (π/2)+

  • 2 years ago
  • 2 years ago

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  1. Jusaquikie Group Title
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    not sure where to go to with this

    • 2 years ago
  2. TuringTest Group Title
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    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\[\Large\lim_{x\to\pi/2^+}\tan x\]

    • 2 years ago
  3. TuringTest Group Title
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    what is\[\lim_{x\to\pi/2}\tan x\]

    • 2 years ago
  4. TuringTest Group Title
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    ?

    • 2 years ago
  5. Jusaquikie Group Title
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    +infinity?

    • 2 years ago
  6. Jusaquikie Group Title
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    .027

    • 2 years ago
  7. TuringTest Group Title
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    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

    • 2 years ago
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    I have no idea where you got that number from....

    • 2 years ago
  9. Jusaquikie Group Title
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    tan(pi/2) lol

    • 2 years ago
  10. TuringTest Group Title
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    I'm gonna take a wild guess and say you left your calculator in degree mode

    • 2 years ago
  11. Jusaquikie Group Title
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    yes

    • 2 years ago
  12. TuringTest Group Title
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    \[\tan x=\frac{\sin x}{\cos x}\]so\[\tan (\pi/2)=\frac{\sin (\pi/2)}{\cos (\pi/2)}=?\]

    • 2 years ago
  13. Jusaquikie Group Title
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    1/0= undefined

    • 2 years ago
  14. TuringTest Group Title
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    right, now what about coming from the right, x>pi/2 will cosince be positive or negative approaching pi/2 from the right?

    • 2 years ago
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    cosine*

    • 2 years ago
  16. Jusaquikie Group Title
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    positive and increasing to 1?

    • 2 years ago
  17. TuringTest Group Title
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    no, what is the cosine of pi/2 ?

    • 2 years ago
  18. Jusaquikie Group Title
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    0 sorry was thinking sin

    • 2 years ago
  19. Jusaquikie Group Title
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    so negative

    • 2 years ago
  20. TuringTest Group Title
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    correct, so as \(x\to\pi/2^+\) we have that \(\cos x\to0\), which means that\[\lim_{x\to\pi/2^+}\tan x=?\]

    • 2 years ago
  21. Jusaquikie Group Title
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    0

    • 2 years ago
  22. TuringTest Group Title
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    no, think in terms of sin and cos

    • 2 years ago
  23. Jusaquikie Group Title
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    anything with Euler's number just confuses me, i'm not sure how to treat it

    • 2 years ago
  24. Jusaquikie Group Title
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    2pi

    • 2 years ago
  25. TuringTest Group Title
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    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?

    • 2 years ago
  26. TuringTest Group Title
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    what is sine approaching? what is cos approaching?

    • 2 years ago
  27. Jusaquikie Group Title
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    1,0

    • 2 years ago
  28. TuringTest Group Title
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    and is that zero being approached from the negative or positive side?

    • 2 years ago
  29. Jusaquikie Group Title
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    negative?

    • 2 years ago
  30. TuringTest Group Title
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    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?

    • 2 years ago
  31. Jusaquikie Group Title
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    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

    • 2 years ago
  32. Jusaquikie Group Title
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    -infinity?

    • 2 years ago
  33. Jusaquikie Group Title
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    no + infinity

    • 2 years ago
  34. TuringTest Group Title
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    |dw:1347837808350:dw|you were right the first time, -infty

    • 2 years ago
  35. TuringTest Group Title
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    positive number (sine) being divided by a small negative number (cosine) is a large negative number

    • 2 years ago
  36. TuringTest Group Title
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    \[\frac1{-0.1}=-10\]\[\frac1{-0.01}=-100\]\[\frac1{-0.001}=-1000\]etc., so as cos x goes to zero from x>pi/2 we approach \(-\infty\)

    • 2 years ago
  37. TuringTest Group Title
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    hence\[\lim_{x\to\pi/2^+}\tan x=-\infty\]

    • 2 years ago
  38. Jusaquikie Group Title
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    ok

    • 2 years ago
  39. TuringTest Group Title
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    so then what is\[\lim_{x\to\pi/2^+}8e^{\tan x}\]

    • 2 years ago
  40. Jusaquikie Group Title
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    zero?

    • 2 years ago
  41. TuringTest Group Title
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    correct :)

    • 2 years ago
  42. Jusaquikie Group Title
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    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

    • 2 years ago
  43. TuringTest Group Title
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    it's fine, much better than just pumping out an answer you won't comprehend hopefully you learned something is the idea ;)

    • 2 years ago
  44. Jusaquikie Group Title
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    yes thanks

    • 2 years ago
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