Explain please.
One solution of the equation is trivial, x=1. I have no clue what the other is and can't seem to calculate it either.
31 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.hint: differentiate the function once. now check at which intervals it increases or decreases. you are supposed to check atleast 1 of the solutions intuitively. now try to make a rough graph (only qualitivative)......and i think you should get it.
you can try once on your own.
@Opt were you able to figure it out from here?
Nope. And I totally forgot about it.
It's hard to figure out the other solution exactly with paper, since natural log is involved
Like Thanos said you have to graph it
same lol
i solved it but completely forgot posting a solution, sorry.
This is a very well framed question.
Just look at the slope, it is zero at one point, positive before that and negative after.
f(x) itself tends to -infinity as x tends to infinity ( -2023x decreases a lot faster for big value of x, logx just increases by 1/x which is almost nothing at big values of x)
f(x) clearly goes to -infinity as x tends to zero and the slope is zero at 1/2023
So clearly it has to cut the x axis at two points!
lmk if you’re able to sketch the graph using this info, else i’ll send a detailed plot and steps
actually, it’ll be just like lnx-x, just translated up by 2023 and decreasing a lot faster!!
Oh, I forgot that linears overtake logarithms for large values. That's where I missed the point.
@πrate this is what the graph looks like on Desmos and Geogebra.
aah
don’t worry it’s not wrong
Looks like x=1
the part going towards -infinity is very close to zero
try lnx-x +1
you agree that this and lnx -2023x +2023 will be the same? or is there any doubt
only rate is different
Wait I'll zoom out to very large x
yes
the one in question is exactly like this, just very very steep
Nvm I forgot to hit enter
lol
Yeah I get it now, but during the exam, just how are we supposed to figure it out?
the age old question 💀
it won’t magically hit you
you’ll see it only after you’ve seen, analysed, plotted 1000s of functions!
i only used this logic
only to realise later that i’ve used this lol
i realised after i typed the explanation
Thanks for the help. I actually had another question I wanted to post in the server, but mind if I ask it here?
that this is lnx-x only
go on?
i’ve to leave in 10-15 mins though
The answer is 8/π³ as per the key, but I couldn't solve it
Tried partial fractions, trigo identities, nothing worked
From my limited experience, obtaining a telescoping series seems to be the way to go, but I can't seem to do it.
i see
looks a bit calculative, i’ll have to try it on pen and paper!
will do after coming back
Alright, ping when you're done please
certainly
create a thread for it
i might forget
I'll close this one.
+solved @πrate @Deleted User
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