Tuesday 20 October 2015

real analysis - Incorrect Chain Rule Proof




I have a valid proof for the Chain Rule, however I do not understand why the 'arguement' given here is incorrect.



enter image description here



enter image description here


Answer



The problem is simply that if $g$ were constant in a neighborhood of $a$, then $g(x)-g(a)=0$ when $x$ is close to $a$, and thus you are dividing by $0$.


No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...