Question

Which limit is the left-hand derivative at \[x=c\]?

Options

• \[\lim_{h\to0^+}\frac{f(c+h)-f(c)}{h}\]

• \[\lim_{h\to0}\frac{f(c-h)-f(c)}{h}\]

• \[\lim_{x\to c}\frac{f(x)-f(c)}{h}\]

• \[\lim_{h\to0^-}\frac{f(c+h)-f(c)}{h}\]

Answer 1

The left-hand derivative uses increments \[h\] approaching zero through negative values. It is therefore written with \[h\to0^-\].