Here's the question you clicked on:
JaySongChang
Find the limit, if it exists. (If an answer does not exist, enter DNE.) Lim x->(pi/2)+ 7e^(tan x)
I thought it would be infinity but apparently infinity is incorrect
\[\tan(\pi /2) = \sin(\pi /2)/\cos(\pi /2) = 1/\cos(\pi /2)\] 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.
The answer does not exist is marked incorrectly for this problem.
I graphed the 7e^(tan x) and it appears that as X approaches pi/2 the graph goes to infinity
Only from the right. From the left it approaches 7
I think the question is only asking for the right hand limit
from right its 0, from left its infinity.
since there is a small + sign the left of the Pi/2
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
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