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JaySongChang

  • 2 years ago

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

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  1. JaySongChang
    • 2 years ago
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    I thought it would be infinity but apparently infinity is incorrect

  2. azolotor
    • 2 years ago
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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.

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

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

  5. azolotor
    • 2 years ago
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    Only from the right. From the left it approaches 7

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

  7. hartnn
    • 2 years ago
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    from right its 0, from left its infinity.

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

  9. JaySongChang
    • 2 years ago
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    right*

  10. hartnn
    • 2 years ago
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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

  11. JaySongChang
    • 2 years ago
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    thanks a lot!

  12. hartnn
    • 2 years ago
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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

  13. hartnn
    • 2 years ago
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    welcome ^_^

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