anonymous
  • anonymous
Find the limit, if it exists. (If an answer does not exist, enter DNE.) Lim x->(pi/2)+ 7e^(tan x)
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I thought it would be infinity but apparently infinity is incorrect
anonymous
  • anonymous
\[\tan(\pi /2) = \sin(\pi /2)/\cos(\pi /2) = 1/\cos(\pi /2)\] 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.
anonymous
  • anonymous
The answer does not exist is marked incorrectly for this problem.

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anonymous
  • anonymous
I graphed the 7e^(tan x) and it appears that as X approaches pi/2 the graph goes to infinity
anonymous
  • anonymous
Only from the right. From the left it approaches 7
anonymous
  • anonymous
I think the question is only asking for the right hand limit
hartnn
  • hartnn
from right its 0, from left its infinity.
anonymous
  • anonymous
since there is a small + sign the left of the Pi/2
anonymous
  • anonymous
right*
hartnn
  • hartnn
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
anonymous
  • anonymous
thanks a lot!
hartnn
  • hartnn
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
hartnn
  • hartnn
welcome ^_^

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