Question

lim 8e^(TanX)
x → (π/2)+

Answer 1

not sure where to go to with this

Answer 2

since\[\Large\lim_{x\to a}e^{f(x)}=e^{\lim_{x\to a}f(x)}\]really all you need to know is the limit\[\Large\lim_{x\to\pi/2^+}\tan x\]

Answer 3

what is\[\lim_{x\to\pi/2}\tan x\]

Answer 4

?

Answer 5

+infinity?

Answer 6

.027

Answer 7

actually it depends on the left and right hand approach
from the left (x<pi/2) cos x>0
from the right (x>pi/2) cos x<0

Answer 8

I have no idea where you got that number from....

Answer 9

tan(pi/2) lol

Answer 10

I'm gonna take a wild guess and say you left your calculator in degree mode

Answer 11

yes

Answer 12

\[\tan x=\frac{\sin x}{\cos x}\]so\[\tan (\pi/2)=\frac{\sin (\pi/2)}{\cos (\pi/2)}=?\]

Answer 13

1/0= undefined

Answer 14

right, now what about coming from the right, x>pi/2
will cosince be positive or negative approaching pi/2 from the right?

Answer 15

cosine*

Answer 16

positive and increasing to 1?

Answer 17

no, what is the cosine of pi/2 ?

Answer 18

0 sorry was thinking sin

Answer 19

so negative

Answer 20

correct, so as \(x\to\pi/2^+\) we have that \(\cos x\to0\), which means that\[\lim_{x\to\pi/2^+}\tan x=?\]

Answer 21

0

Answer 22

no, think in terms of sin and cos

Answer 23

anything with Euler's number just confuses me, i'm not sure how to treat it

Answer 24

2pi

Answer 25

ignore Euler's number, it could be any exponential base, the answer would be the same...\[\lim_{x\to\pi/2^+}\frac{\sin x}{\cos x}=?\]what is sine approaching?
what is cos approaching?

Answer 26

what is sine approaching?
what is cos approaching?

Answer 27

1,0

Answer 28

and is that zero being approached from the negative or positive side?

Answer 29

negative?

Answer 30

correct, so considering that\[\lim_{x\to\pi/2^+}\tan x=\lim_{x\to\pi/2^+}\frac{\sin x}{\cos x}\to\frac10\]and that that zero is being approached from the negative side, what is the limit?

Answer 31

i can't visualize it and i'm not sure how to graph it in my calculator so i'm trying to relate it to the unit circle

Answer 32

-infinity?

Answer 33

no + infinity

Answer 34

you were right the first time, -infty