Question

How do you: Evaluate the lim x-->pi/2 e^tant

Answer 1

Check what you wrote, is it suppose to be e^tan(x)?

Answer 2

What does the tangent do at pi/2?

Answer 3

Maybe @mathis1, the paper I have has a t not x

Answer 4

If that is the case, there is no x to plug in, and the limit x->pi/2 = e^tant

Answer 5

If it really just has a t....then the function isn't affected no matter where x approaches...so it would just be e^tant

Answer 6

so it is lim t->pi/2

Answer 7

I copied it correctly, it is lim x-->pi/2 e^tant

Answer 8

If there is a typo, it's on the worksheet I copied from.

Answer 9

Well if the limit and the tan(x) are not the same variable, it is like I said before, the variables are not the same, so the limit is just the e^tant. If they are the same variable, then you need to think, what part of the equation is the most greatly affected, in this case the tanx. So, what does tanx do at pi/2?

Answer 10

\[\lim _{t \rightarrow \frac{ \pi }{ 2 }}e ^{\tan t}\]
Is that it?

Answer 11

A two sided limit does not exist... \(\tan t\to\infty\) as \(t\to\pi/2^-\) so approaching from the left should give us \(e^{\tan t}\to\infty\). From the right, however, \(\tan t\to-\infty\) and thus \(e^{\tan t}\to 0\)

Answer 12

Honestly, I'm not sure what tan x does at pi/2.

Answer 13

@NoelGreco I'm not sure if the paper I have has a typo or if it is supposed to be x and t

Answer 14

It's a typo because t could not care less what x is doing.

Answer 15

@wesdg1978 \(\cos t\to0\) as \(t\to\pi/2\) yet \(\sin t\to1\) so \(\tan t=\sin t/\cos t\to\pm\infty\) depending on whether you approach it from where \(\cos t<0\) or \(\cos t>0\)

Answer 16

\[\tan x=\frac{ \sin x }{ \cos x }\]

What does the denominator approach as the variable goes to zero.

Answer 17

1

Answer 18

Sorry. What does the denominator approach as the variable goes to pi/2?

Answer 19

0

Answer 20

Good.

Answer 21

Tan pi/2 then is what?

Answer 22

If the denominator is 0, then it would be undefined, right?

Answer 23

Yes, but for purposes of finding a limit, let's say infinity.

Now we have \[e^{\infty}\]

Answer 24

What's the limit?

Answer 25

I have to turn in for the night Any last thoughts?

Answer 26

My internet went out for like 5 minutes. Is it e^infinity is infinity

Answer 27

My apologies, my computer locked up and my internet went out.

Answer 28

Bingo! Best answer is DNE (does not exist) the limit is +inf from the left, and -inf from the right.

Learn those trig graphs! It'll pay off.

Answer 29

Thank you very much!

Answer 30

Limits, trig, and a curious student? - my pleasure.

Answer 31

After this test tomorrow, I'm going to go back and refresh memory with trig, any suggestions on the best way to learn trig graphs @NoelGreco ?