## anonymous 3 years ago Find the limit, if it exists. (If an answer does not exist, enter DNE.) Lim x->(pi/2)+ 7e^(tan x)

1. anonymous

I thought it would be infinity but apparently infinity is incorrect

2. 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.

3. anonymous

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

4. anonymous

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

5. anonymous

Only from the right. From the left it approaches 7

6. anonymous

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

7. hartnn

from right its 0, from left its infinity.

8. anonymous

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

9. anonymous

right*

10. 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

11. anonymous

thanks a lot!

12. 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

13. hartnn

welcome ^_^