Continuity & Differentiability | L4 | 10 important theorems, results & concepts inc. Bolzano | IVT

Continuity & Differentiability | L4 | 10 important theorems, results & concepts inc. Bolzano | IVT

00:00:00 Bolzano's theorem
00:06:04 Intermediate value theorem
00:10:00 Weierstrass theorem
00:11:35 Sign preserving property
00:12:41 Continuity of integrable functions
00:14:18 Continuity of inverse function
00:17:00 Continuity at rational and irrational points
00:30:11 Continuity at an isolated point
00:32:00 Note on continuity of composite functions
00:34:58 Continuous extension of a function
00:37:40 Miscellaneous questions

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[c--dakshsharma]

I usually dont comment but the level of knowledge you inhibit and provide us in an exponential manner is just wonderful hope you will be back soon sir for us 2025 asps

[rajanisinha]

t 0:27 4:18 t 6:24 t 10:21 t 12:48 inverse cont. 15:03 28:46 30:53 32:32 37:38 40:27

[akshat]

Sir at 29:55 dy/dx of the second fxn become zero at x = 2.... Which means either the fxn has either minima or maxima at that point ....
And curve will become horizontal at that point wrt x axis.
Correct me if I am wrong because you said graph will become vertical.

Thank you for amazing learning experience.
Love from Uttar Pradesh 🙏