Theorem for limits of composite functions: when conditions aren't met | AP Calculus | Khan Academy

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Suppose we are looking for the limit of the composite function f(g(x)) at x=a. This limit would be equal to the value of f(L), where L is the limit of g(x) at x=a, under two conditions. First, that the limit of g(x) at x=a exists (and if so, let's say it equals L). Second, that f is continuous at x=L. If one of these conditions isn't met, we can't assume the limit is f(L).

[avrohomhousman]

1:28 can you please explain this? Why are you approaching 0 in G(x) from the left, but approaching 2 in F(x) from the right? Is approaching from above the same as approaching from the right or does it depend on the shape of the line? it would be helpful if you were more consistent with the words you use.

[imranahmadov]

3:05 So what analysis can we talk about once limit of g(x) does not exist?

[FigureZ]

I love how it's the same guy in every video since like 2015.

[HeyKevinYT]

Thanks Mr Sal Khan! This will be useful for the AP Calculus AB and BC exams, I suppose

[TheScienceCube]

I really like the random splatter of writing on the black board

[adibahsyaysa]

can someone tell me whats the answer for the last question and how to do it :(

[iacpkdf]

trust me im 14 and had to go through this torture for 7 years

[thanaa]

Why should the function be continuous? Isn't it enough for it to be defined? Can't we input the real value of the function f and not the value it's approaching?

[SwissBanjo]

"limit" and not "limes" ??

[francescoejlli]

Ho what's the name of the blackboard software you use?