Question

Limit of artan(e^x) as x approaches 0

Answer 1

@Astrophysics

Answer 2

is it just a rule that it equals pi/2 every time? xD

Answer 3

isn't it pi/4 ?

Answer 4

\(\color{#000000 }{ \displaystyle \lim_{x\to0}~\arctan(e^x) }\)

Yes, but it is a direct answer too.

Answer 5

Nein, it's pi/2

Answer 6

pi/4 is correct, which you will notice by graphing.

Also, \(\color{#000000 }{ \displaystyle \lim_{x\to0}~\arctan(e^x)=\arctan(1)=\pi/4 }\)
by a direct sub.

Answer 7

I am saying this, not to confuse with the incorrect answer.

Answer 8

we can check like this if in doubt: tan (pi/4)=1

Answer 9

hmmm

Answer 10

tan(pi/2) is undefined because cos(pi/2) = 0

tan(x) = sin(x)/cos(x)

Answer 11

In class when we went over this the prof presented this by just saying
lim as x approaches 0 artan(e^x) = pi/2
as if it were a rule though.

Like wolframalpha also says it is pi/4 but the man said pi/2 xD

Answer 12

And..the homework agrees o.o -.- o.o

Answer 13

hey there its x tends to infinity..

Answer 14

More evidence:
http://www.wolframalpha.com/input/?i=limit+x--%3E+0+arctan(e%5Ex)

Answer 15

u said x tends to zero

Answer 16

oh crap. Sorry!

Answer 17

Oh, infinity, indeed would change it :)

Answer 18

haha I was confused too because I kept getting pi/4 as well. I am so sorry xD

Answer 19

its ok..

Answer 20

\(\color{#000000 }{ \displaystyle \lim_{x\to\infty}\arctan(e^x) =\pi/2 }\)
that would be right

Answer 21

Ok, and how do we get that it's pi/2? hehe

Answer 22

First, you might want to review the domain and range of arctan(x)

Answer 23

so it's by looking at the graph and just knowing that?

Answer 24

Substitute e^x as t

Answer 25

Yes, exactly.