Limits of Composite Functions

You evaluate the limit for the inner function first, then you evaluate the limit for the outer function,

Example ${\lim }_{x\to 2^{+}}f(g(x))$

${\lim }_{x\to 2^{+}}f(g(x))\equiv {\lim }_{x\to {\lim }_{x\to 2}g(x)}f(x)$ First find ${\lim }_{x\to 2^{+}}g(x)=2^{-}$ Since its $2^{-}$, we will approach ${\lim }_{x\to 2^{-}}f(x)=1^{+}$ We can just say its $1$

DNE Evaluation

If you think that the limit is DNE, be very confident that it is. Try both one-sided limits and see if they really are different.