## anonymous 5 years ago find the limit lim x approaches (pi/2) e ^tanx

1. mathteacher1729

What is the limit as x approaches pi/2 for tan(x) ? (if one exists)

2. anonymous

$\lim \rightarrow \pi/2 e^tanx$

3. anonymous

from which direction?

4. anonymous

$\pi/2$

5. anonymous

if no direction is given then there is no limit.

6. anonymous

to $e^{tanx}$

7. anonymous

$tan(\frac{\pi}{2})$ is undefined

8. anonymous

$lim_{x->\frac{\pi}{2}}tan(x)$

9. anonymous

does not exist.

10. anonymous

if you go from the right you get $-\infty$ for the left you get $\infty$

11. mathteacher1729

See what's happening ... as we approach from the left, we go to negative infinity. As we approach from the right, we go to positive infinity. So you have to specify a direction or there is no limit.

12. anonymous

but it has the inverse long of e

13. anonymous

nice picture!

14. anonymous

e ^tanx

15. mathteacher1729

rmalik2 -- do you know what the graph of tan(x) looks like from say x = 0 to x = pi ? This is VERY important for understanding this problem. Please see the picture, or use your graphing calculator to graph this function.

16. anonymous

if you look at the picture you will see that in one direction you go to -infinity and in the other you go to infinity. so you cannot compute this limit. in one direction you will get e to powers getting bigger and bigger which will grow infinitely large. in the other direction you will get e to powers going to -infinity which will give values closer and closer to 0. so no limit!

17. anonymous

but it has the invese log with is e to the power of tan(x)....i understand thegraphing chart but

18. mathteacher1729

If you go that route you are led into the land of complex numbers and multiple solutions. While this is super interesting.. it is probably not where your class is going. :( Unless a direction is specified, there is no limit.