Mathematics

Problem

For a piecewise-defined function, the derivative of

f

at a point

x=a

is most directly defined as which of the following limits, provided the limit exists? a)

\displaystyle \lim_{h\to 0^+}\frac{f(a+h)-f(a)}{h}

\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h}

\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a-h)}{2h}

\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h^{2}}