Question

find the limit
lim x approaches (pi/2) e ^tanx

Answer 1

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

Answer 2

\[ \lim \rightarrow \pi/2 e^tanx\]

Answer 3

from which direction?

Answer 4

\[\pi/2\]

Answer 5

if no direction is given then there is no limit.

Answer 6

to \[e^{tanx}\]

Answer 7

\[tan(\frac{\pi}{2})\] is undefined

Answer 8

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

Answer 9

does not exist.

Answer 10

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

Answer 11

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.

Answer 12

but it has the inverse long of e

Answer 13

nice picture!

Answer 14

e ^tanx

Answer 15

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.

Answer 16

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!

Answer 17

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

Answer 18

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.