how to show the following equality holds.

Oct 2012
17
0
london
any hints to solve the following !!

Show that \(\displaystyle f(x)\) is the derivative of\(\displaystyle f(.)\) at\(\displaystyle x\) if and only if \(\displaystyle lim_{h \to 0} \sup_{|t|\leqslant h} \frac{|f(x+t)-f(x)-tf^{'} (x)|}{h} = 0 \)
 
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