- #1
songoku
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- 335
- Homework Statement
- Please see below
- Relevant Equations
- Limit
Derivative
My attempt:
Since ##\frac{f(a+h)-f(a-h)}{2h}-f'(a)=O(h^2)## as ##h \to 0##, then:
$$\lim_{h \to 0} \frac{\frac{f(a+h)-f(a-h)}{2h}-f'(a)}{h^2} < \infty$$
So
$$\lim_{h \to 0} \frac{\frac{f(a+h)-f(a-h)}{2h}-f'(a)}{h^2} = \lim_{h \to 0} \frac{f'(a)-f'(a)}{h^2}=0 < \infty$$
Because the value of the limit is zero, it is true that ##\frac{f(a+h)-f(a-h)}{2h}-f'(a)=O(h^2)## as ##h \to 0##
Is this even correct?
Thanks