I believe I understand this question but I am stuck at what seems to be a "last part."
Here is the question: Suppose that the function $f: \mathbb{R} \rightarrow \mathbb{R}$ is differentiable at $x_o$. Analyze the following limit: $\lim_{h\ \rightarrow 0} \frac{f(x_o + h) - f(x_o -h)}{h} $.
Analysis:
Observe that $\lim_{h\ \rightarrow 0} \frac{f(x_o + h) - f(x_o -h)}{h} = \lim_{h\ \rightarrow 0} \frac{f(x_o + h) - f(x_o) + f(x_o) -f(x_o -h)}{h} $. Then, applying limit rules, we see that $\lim_{h\ \rightarrow 0} \frac{f(x_o + h) - f(x_o) + f(x_o) -f(x_o -h)}{h} = \lim_{h\ \rightarrow 0} \frac{f(x_o + h) - f(x_o)}{h} + \lim_{h\ \rightarrow 0} \frac{f(x_o) -f(x_o -h)}{h} = f'(x_o) + \lim_{h\ \rightarrow 0} \frac{f(x_o) -f(x_o -h)}{h}$
It is here that I am stuck. How do I deal with that right-most limit directly above, after the "plus"? Also, is this what was desired in terms of "analysis" ?
thanks