limits 3
i tried taking the limit as L and then log both sides to get -->
log L = 1/n * sum (log (r/n))
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then i applied stolz cessaro theorem but that doesnt give the right ans
@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.pls give solution without sterling approximation or limit of a sum
After this use limit of a sum as integral with bounds 0 and 1.
Oh sorry :/
Padha nahi abhi ....
@SirLancelotDuLac beyond the scope of jee
??
Nope the sum of limit to integral is it Im pretty sure but yea.. :/
It would give the answer as integral of log(x) from 0 to 1 which is x(lnx-1) from 0 to 1 which is -1. So the limit L=1/e
Imma try to solve it without using this too so...
well keeping it open then
Mere sir was saying integration me padhayenge
I'm not gonna lie, sterling approximation or limit of a sum seems the only way. Considering how sterling is not in jee (last I remember), limit of the sum is the only nice way to approach this :/
limit of sum se hi bhejdo in future kaam aayega
$\frac{1}{n} \sum{1}^{n} log(\frac{r}{n})=\int{0^{+}}^{1} log(x)dx=\frac{1}{e}$
SirLancelotDuLac
can u briefly explain how this works
1/n becomes dx and r/n becomes x and we change the summation to integral with appropriate limits
Oh sorry mb. When you think of integration, you are basically dividing the graph into infinitisemally thin strips and adding the sum of areas of these small infinitisemal areas right?
bruh ik what integration is
i wanted to know how do u "think" of this conversion
Now think of it this way: Consider a rectangle of breadth 1/n on the x-axis from origin to x=1/n and height f(1/n) on the y-axis. Its area if f(1/n).(1/n). Now consider another rectangle from x=1/n to 2/n and height f(2/n), its area is f(2/n).(1/n)
so this only works for the obtained format
Similarly, the sum of all the areas in this way turns out to be 1/n sum (from 0 to n) f(r/n)
If the integration is from 0 to 1.
In general $\frac{1}{n} \sum{mn}^{kn} f(\frac{r}{n})=\int{m}^{k}f(x).dx$
Ik I was just tryna open with that 😭
SirLancelotDuLac
Yep, this ☝️
Do search up left and right reimann sums to gain more insight.
Iirc one time they asked a question on the difference too.
application of integration
interesting concept
btw needed some help
sat and sun i have phase test
carboxylic acid , aod, electrical instruments and rc (only practice) karna hai
+revision ofc
how do i prioritise
my math is WEAK btw
What is electrical instruments and rc?
Like capacitor and shi?
potentiometer and stuff
and rc circuit problems
how did u go out of touch so soon 💀
I mean, depends on a lot of factors tbh. If its like too advanced, focus on the strong portions and stuff. If its a mains pattern test, try to cover the whole syllabus.
saturday mains sunday adv
Oh...
Yea man, idk how to go on about consecutive tests :sweaty:
soo much work to do is just making my mind not do any work 😭
But yeah, I feel like with the papers in '25, a strong math (like calculation wise too) can give you a lot of edge over others.
ill try to cover up major portion of carboxylic and maybe , just maybe a bit of phy
and then aod tomorrow
unrelated but what was your adv rank
Ehh it was 4.1k
ohh
so where u going then
Prolly iit tirupati
cse?
Yep.
W ig
blunders on paper day or smthing?
Thanks man 🙏
Yep.
But tbh I should also have been better prepared in hindsight
Like given more varieties of mocks and stuff.
yeah that matters a lot
mains %ile not giving much?
99.9x iirc
My biggest error was giving tests where I was scoring a lot, but not giving those where I was scoring less.
I could get nitt ot nitk, but trichy was not feasible (due to location) and I've heard a lot about nitk 💀
arent trichy and tirupati close tho
mb 💀
Tirupati is in andhra, trichy is further south ig.
hmm
what did u solve for maths
i am finding my module a bit too hard
(invictus)
Very varied tbh. In 11th I just did modules, bansal sheets and black book. (My dumb ahh didn't do pyqs)
In 12th I used to do sheets, sameer bansal for calc, research some books in related fields (I also did success magnet for 11th in 12th)
I tried to rush pyqs when it was getting too late.
pyqs toh meien bhi bohot kam kare hai
sign from god to start them now
2024 tak ke saare kie ??
i was thinking of doing up until 2020 or 2021
so that i can give rest of the papers as mocks
Tried to, yeah. But ended up leaving some topics for mains and advanced in the end.
I actually did this.
I did not do salt analysis or p-block
Or d-block in detail
on the other hand i have and probably will face adv pyqs in books and coaching tests
Basically left inorganic becoz time...
so just do em all and focus on coaching mocks
so former or latter ?
Um tbh idk in 11th and early 12th I did not give many mocks (Actually, my coaching didn't take any) :/
So no idea...
"mocks" se i mean end of the year full syll mocks for jee adv
For advanced do pyqs before giving mocks to be like, mentally prepared.
all the pyqs it is then
I mean, you can try but the too old ones are sort of...
Too old ig.
Like the ones from aieee-jee or whatever it was called.
ill do coaching archive
alr thanx
marking it solved now
+solved @SirLancelotDuLac
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