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.

[yzhjzgx]

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.

[cocoa]

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

[jingbinyu]

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

[seekerm]

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

[santoshbanerjee]

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

[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.

[bhavishyapandey]

sir please translate your every vedio in hindi