Question

Find the limit, if it exists. (If an answer does not exist, enter DNE.)

Lim
x->(pi/2)+ 7e^(tan x)

Answer 1

I thought it would be infinity but apparently infinity is incorrect

Answer 2

\[\tan(\pi /2) = \sin(\pi /2)/\cos(\pi /2) = 1/\cos(\pi /2)\] 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.

Answer 3

The answer does not exist is marked incorrectly for this problem.

Answer 4

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

Answer 5

Only from the right. From the left it approaches 7

Answer 6

I think the question is only asking for the right hand limit

Answer 7

from right its 0, from left its infinity.

Answer 8

since there is a small + sign the left of the Pi/2

Answer 9

right*

Answer 10

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

Answer 11

thanks a lot!

Answer 12

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

Answer 13

welcome ^_^