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JaySongChang

Find the limit, if it exists. (If an answer does not exist, enter DNE.) Lim x->(pi/2)+ 7e^(tan x)

  • one year ago
  • one year ago

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  1. JaySongChang
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    I thought it would be infinity but apparently infinity is incorrect

    • one year ago
  2. azolotor
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    \[\tan(\pi /2) = \sin(\pi /2)/\cos(\pi /2) = 1/\cos(\pi /2)\] Now you can take the left and right hand limits of this to find out if they are equal. In this case they are not so the limit does not exist.

    • one year ago
  3. JaySongChang
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    The answer does not exist is marked incorrectly for this problem.

    • one year ago
  4. JaySongChang
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    I graphed the 7e^(tan x) and it appears that as X approaches pi/2 the graph goes to infinity

    • one year ago
  5. azolotor
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    Only from the right. From the left it approaches 7

    • one year ago
  6. JaySongChang
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    I think the question is only asking for the right hand limit

    • one year ago
  7. hartnn
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    from right its 0, from left its infinity.

    • one year ago
  8. JaySongChang
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    since there is a small + sign the left of the Pi/2

    • one year ago
  9. JaySongChang
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    right*

    • one year ago
  10. hartnn
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    see, from right means x > pi/2 x is in 2nd quadrant where tan x is negative. also, tan pi/2 = infinity so, e^{-infinity} will tend to 0

    • one year ago
  11. JaySongChang
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    thanks a lot!

    • one year ago
  12. hartnn
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    from left means x< pi/2 x is in 1st quadrant where tan x is positive. also, tan pi/2 = infinity so, e^{infinity} will tend to infinity

    • one year ago
  13. hartnn
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    welcome ^_^

    • one year ago
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