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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:05:42
> you might have to use exponent laws here as well
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:06:38
once you answer this, we might very well be able to start with your actual question
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:07:12
Ik it's supposed to be a^b
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0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:07:17
Yep
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:07:19
Just not clearly getting how
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:07:24
okayyy
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:07:25
In my head
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:07:30
It should be
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:07:33
b * a
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0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:07:40
So, you have: $e^{b \ln a}$ right?
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help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:07:42
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:07:45
y
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:07:53
next, you use the exponent laws
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:08:32
$e^{b \ln a} = e^{b \times \ln a} = (e^{\ln a})^b$
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help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:08:34
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:08:39
Got it!?
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:09:00
let's just another example
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:09:02
like
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0
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:09:07
wait
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:09:11
hmm
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1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:09:12
let me try to use the bot
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:09:22
Let's take:
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:09:57
$2^{3\log_2 7}$
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help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:10:13
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:10:17
$4^{6 \times \x} = (4^{\x})^6$
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0
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help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:10:19
**pinto** Compile Error! Click the :errors: reaction for more information. (You may edit your message to recompile.)
https://cdn.discordapp.c…991092314133.png
467079991092314133.png
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1
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:10:38
$4^{6 \times x} = (4^{x})^6$
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1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:10:40
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:10:43
Right ?
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1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:10:47
yes
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:10:53
that's what the exponent laws say
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:10:54
that's what I wanted
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0
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:10:58
Oh okay
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:11:05
No doubts then
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0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:11:10
hence we could write
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:11:12
$e^{b \ln a} = e^{b \times \ln a} = (e^{\ln a})^b$
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:11:12
Got it
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:11:14
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:11:24
$= a^b$
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:11:26
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:11:30
Got it?
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:11:33
yes yes
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:11:40
100% sure?
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:11:45
yes
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:11:51
I said before I wasn't understanding
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:11:52
Now, back to the actual question
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:11:58
If I hadn't got it I would tell
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:12:06
$\lim_{x \to \frac{\pi}{2}} (\sin x - \cos x)^{\tan x}$
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:12:09
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:12:13
Right?
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1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:12:15
yes
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:12:33
We use the same trick to send the stuff inside the parenthesis to the exponent
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:12:35
okay?
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:12:46
ok
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:12:49
don't say anything
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:12:53
let me try to work this out
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:12:57
hmmm
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:12:59
then you say if I got it right
1
0
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:13:02
okie
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:13:06
Just with this tip
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:14:16
okkkkk
1
0
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:14:41
tough
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:14:47
Cause it's so different
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:15:10
nope
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:15:13
@Ansh_
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:15:17
Couldn't do it
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:15:34
oop
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:16:21
So we do the same trick and get
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:16:29
$\lim_{x \to \frac{\pi}{2}} (\sin x - \cos x)^{\tan x}$
0
1
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null
null
null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:16:31
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:16:39
that's the same we had
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:16:56
$=\lim_{x \to \frac{\pi}{2}} e^{\tan x \ln (\sin x - \cos x)}$
0
1
706,934,233,012,371,600
Ansh_
3502
Arya
false
496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:17:11
oh we need to change base
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:17:13
alright
1
0
null
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:17:16
makes so much sense
1
0
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null
null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:17:18
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:17:23
Makes sense?
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:17:28
yes
1
0
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:18:58
Yep
0
1
null
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:19:08
now, which indeterminate form do you see?
0
1
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help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:19:31
let me see
1
0
null
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:20:54
ln(1)
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:20:56
= 0
1
0
null
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null
null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:21:05
oo * 0?
1
0
null
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null
null
null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:21:23
Yep
0
1
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:21:40
the exponent now has the indeterminate form: $\infty \cdot 0$
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:21:43
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:22:13
Next, my question is: which indeterminate form do you want this to become... that will make it most comfy for you
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:23:35
That's a tricky question
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:23:42
👀
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:23:48
I like 0/0 or oo/oo
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:23:51
For L'Hopitale
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:23:53
I guess
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:23:53
Great
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:23:56
$=\lim_{x \to \frac{\pi}{2}} e^{\tan x \ln (\sin x - \cos x)}$
0
1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
510,789,298,321,096,700
TeXit
02/04/2022 15:23:58
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
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null
496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:24:20
the ln part is 0 already, what would you do to make the exponent 0/0 form
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1
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:27:46
@Ansh_
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
467,079,991,092,314,100
pinto
02/04/2022 15:27:54
I don't seem to be getting anywhere
1
0
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496
help-10
73a113a93de543d7898ff8ae1f351ad9
706,934,233,012,371,600
Ansh_
02/04/2022 15:27:56
$=\lim_{x \to \frac{\pi}{2}} e^{\frac{\ln(1 - \cot x) - \ln(\sin x)}{\cot x}}$
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