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anonymous

  • 5 years ago

find the limit lim x approaches (pi/2) e ^tanx

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  1. mathteacher1729
    • 5 years ago
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    What is the limit as x approaches pi/2 for tan(x) ? (if one exists)

  2. anonymous
    • 5 years ago
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    \[ \lim \rightarrow \pi/2 e^tanx\]

  3. anonymous
    • 5 years ago
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    from which direction?

  4. anonymous
    • 5 years ago
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    \[\pi/2\]

  5. anonymous
    • 5 years ago
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    if no direction is given then there is no limit.

  6. anonymous
    • 5 years ago
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    to \[e^{tanx}\]

  7. anonymous
    • 5 years ago
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    \[tan(\frac{\pi}{2})\] is undefined

  8. anonymous
    • 5 years ago
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    \[lim_{x->\frac{\pi}{2}}tan(x)\]

  9. anonymous
    • 5 years ago
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    does not exist.

  10. anonymous
    • 5 years ago
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    if you go from the right you get \[-\infty\] for the left you get \[\infty\]

  11. mathteacher1729
    • 5 years ago
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    See what's happening ... as we approach from the left, we go to negative infinity. As we approach from the right, we go to positive infinity. So you have to specify a direction or there is no limit.

  12. anonymous
    • 5 years ago
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    but it has the inverse long of e

  13. anonymous
    • 5 years ago
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    nice picture!

  14. anonymous
    • 5 years ago
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    e ^tanx

  15. mathteacher1729
    • 5 years ago
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    rmalik2 -- do you know what the graph of tan(x) looks like from say x = 0 to x = pi ? This is VERY important for understanding this problem. Please see the picture, or use your graphing calculator to graph this function.

  16. anonymous
    • 5 years ago
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    if you look at the picture you will see that in one direction you go to -infinity and in the other you go to infinity. so you cannot compute this limit. in one direction you will get e to powers getting bigger and bigger which will grow infinitely large. in the other direction you will get e to powers going to -infinity which will give values closer and closer to 0. so no limit!

  17. anonymous
    • 5 years ago
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    but it has the invese log with is e to the power of tan(x)....i understand thegraphing chart but

  18. mathteacher1729
    • 5 years ago
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    If you go that route you are led into the land of complex numbers and multiple solutions. While this is super interesting.. it is probably not where your class is going. :( Unless a direction is specified, there is no limit.

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