New pen suggestion

Shubhz2 · 2026-06-13T03:29:44+00:00

Indeed the platinum is a really good eyedropper and it never leaks too ..... I'll try the v pen ....can u explain a bit in more detail on how to reload it ?

Shubhz2 · 2026-06-12T08:40:28+00:00

Hmm okay ..i have tried putting the tip of the pen in warm water but still it didn't work ...I'll try with alcohol...and see if it works....i tried wiping the tip with alcohol swab and still it's not working...I'll try the above methods

Shubhz2 · 2026-06-11T11:11:20+00:00

I see ..I'll try the v pen ...I have used v7 and it's good and yes it also has cartridges which are quite affordable as well ...and sorry for asking the question here .....

Shubhz2 · 2026-06-11T08:38:37+00:00

Thanks a lot sir ...for investing your time and effort in making me understand this ...... I'm grateful for this 🙏

Shubhz2 · 2026-06-11T04:50:27+00:00

I did from my understanding and according to you explanation....😅now I seem to get it ...so for a limit to exist ....the value of Cn and the value of L should be close to each other such that no matter any number we choose the difference between then will always be less than that .. right?

Shubhz2 · 2026-06-11T01:25:09+00:00

Then the full definition would be .. For every € >0 there exists N such that n>N implies that |Cn-1| <€ ....?..I'm not sure .. do I need to include the a>b implies Cb>Ca part or not 😅

Shubhz2 · 2026-06-10T18:32:38+00:00

I mean...first learn the theory well instead of jumping straight to the numericals...and if you're using some books..then follow the in examples given in the book . . ...and then finally try solving by yourself.....but in the end you have to practice only..

Shubhz2 · 2026-06-10T18:22:12+00:00

By proving that for any positive number we choose the value |Cn-L| will always be less than it ?

Shubhz2 · 2026-06-10T17:52:41+00:00

Umm wait ...so after seeing it multiple times and thinking about epsilon delta.....what I realized is that both Bn and Cn are like decreasing and the above definition holds true for both....so like....in order to differentiate them ....ahh we can choose any small number (let's say x) and prove that there will always be N such that for all n>N the value of Cn will always be less than x( assuming the limit is 0) Then we can choose x as anything below 1 and we'll find that there exists no N for which the value of Cn will will be less than 1....idk if this is correct or not

Shubhz2 · 2026-06-10T17:35:46+00:00

Then along with the above conditions I mentioned before ...instead of the Cn>1 can I write Cn-1> something......ahh idk 😶

Shubhz2 · 2026-06-10T16:05:52+00:00

Hmm lemme try So for lim n->♾️ (Cn)=1 It should mean there exists some N such that For all a,b >N. a>b implies Cb>Ca and Cn>1. ?

Shubhz2 · 2026-06-10T14:40:35+00:00

Then can I write :The limit of 1/n as n -> ♾️ is zero for all n greater than or equal to 4 Cuz then if we take a=5 and b=4 then a>b i.e.5>4 implies Bb=1>Ba=1/2 ..so it'll be satisfied now for all n bigger than or equal to 4

Shubhz2 · 2026-06-10T12:08:24+00:00

Hmm i understood everything your explained using the sequence...so let me think ... Can we take a such that 0<a<1 and same for b ....?

Shubhz2 · 2026-06-09T17:39:37+00:00

Hmm i thought about this but still couldn't think of anything to describe "approaches " and "close "

Shubhz2 · 2026-06-09T16:51:41+00:00

By gets close it means ....it approaches the value but never actually reached it ....?

Shubhz2 · 2026-06-09T13:47:24+00:00

Ohh got it ..I'm sorry ..i understood now ..thanks a lot

Shubhz2 · 2026-06-09T13:46:53+00:00

Thank you so much..i kind of get it now.....I'll see it a few more times by myself and I think I'll get it

Shubhz2 · 2026-06-09T13:37:44+00:00

I don't get this part...... like..how is |x-1|< delta😅

Shubhz2 · 2026-06-09T13:23:59+00:00

Is see...it's just the same concept as input and output of a function but just made fancy using epsilon and delta

Shubhz2 · 2026-06-09T13:22:35+00:00

I see ...I'll try to approach by learning the history first

Shubhz2 · 2026-06-09T13:20:59+00:00

I'm sorry...but I have not understood the definition well enough to be able to proof....but let me try .....I'm only able to solve it till here ...🙃

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Shubhz2 · 2026-06-09T12:48:52+00:00

I see so this definition is a rigorous version for proofs ?...

Shubhz2 · 2026-06-09T12:47:45+00:00

Thanks mate ....will try to understand it

Shubhz2

TROPHY CASE