8. Proving the Limit of a Composite Function

Here we essentially prove that a limit within a limit can exist in the same way that a function within a function can exist and this limit is important as it is the basis for proving other limits as well.

[@cocoa1996]

That was the only proof that got through to me! nice work!

[@user-yz5hj3zg2x]

I reviewed a lot of sources and I'm glad I didn't give up, because I finally found your video and your explanation was exactly I exactly what I was looking for. Thus, all the searching was worth it. Thank you very much. I'll leave my Like and subscribe.

[@santoshbanerjee3407]

Thanks for the proof. This could be generalized to the case where f is not necessarily continuous at u=L (in this video, we are implicitly assuming that f is continuous at u = L, as we are being told that lim f(u) = f(L) as u->L). But if we simply say that lim f(u) as u->L = F, even then it should be provable, using similar argument as made in the video, that lim f(g(x)) = F as x -> c

[@jingbinyu8136]

This is soooo clear. Thank you so much for your narration!

[@seekerm8349]

Thank you. I had a doubt about the choice of delta_1 for epsilon which you specifically helped out with.

[@urthogie]

Hey, this was a helpful proof. However I'd recommend slowing down at the end, where there are several logical implications to chain together, it's the trickiest part.

[@jrtthamasha7306]

Thankyou😌

[@arthurgames9610]

Great!

[@xiangli9588]

You are amazing.

[@itsthesame]

Very nice!

[@bhavishyapandey8155]

sir please translate your every vedio in hindi