MAT 213 Lecture Notes - Lecture 14: Implicit Function Theorem, Dependent And Independent Variables
Document Summary
Provide a generalization to each of the key terms listed in this section. When it comes to showing the proof, there is a change in t in t is producing the chances of both. X while in x along with y in y. When you divide both of the given equation, by t, then the following can be created: Now, if you let t 0, then that means that the following would be created thanks to both g being di erentiable (making it automatically continuous): X = g(t + t) g(t) 0. On the other hand, if y 0; if that is the case, then both 1 0 and 2 0, which would create the following: = (lim t 0 ( 1)) lim t 0 (cid:2) x (cid:16) f dt (cid:1) + (cid:16) f. X(cid:17)(cid:0) dx dt (cid:1) + (cid:16) f (cid:16) f (cid:16) f. T (cid:3) + (lim t 0 ( 2)) lim t 0 h y.
