∵
| lim |
| h→∞ |
| 1 |
| h |
∵连续不一定可导，例如：f（x）=|x|在x=0处不可导．
∴A选项不正确
∵
| lim |
| h→0 |
| f(a+2h)−f(a+h) |
| h |
∴
| lim |
| h→0 |
| f(a+2h)−f(a+h) |
| h |
∴B选项不正确
∵
| lim |
| h→0 |
| f(a+h)−f(a−h) |
| 2h |
| 3f′(a) |
| 2 |
∴C选项不正确
∴根据排除法得到
D选项正确
故选：D
| lim |
| h→+∞ |
| 1 |
| h |
| lim |
| h→0 |
| f(a+2h)−f(a+h) |
| h |
| lim |
| h→0 |
| f(a+h)−f(a−h) |
| 2h |
| lim |
| h→0 |
| f(a)−f(a−h) |
| h |
| lim |
| h→∞ |
| 1 |
| h |
| lim |
| h→0 |
| f(a+2h)−f(a+h) |
| h |
| lim |
| h→0 |
| f(a+2h)−f(a+h) |
| h |
| lim |
| h→0 |
| f(a+h)−f(a−h) |
| 2h |
| 3f′(a) |
| 2 |