lim |
x→0 |
f(x0+x)−f(x0) |
x |
∴
lim |
x→0 |
f(x0+x)−f(x0−3x) |
x |
lim |
x→0 |
f(x0+x)−f(x0)+f(x0)−f(x0−3) |
x |
=
lim |
x→0 |
f(x0+x)−f(x0) |
x |
lim |
x→0 |
f(x0−3x)−f(x0) |
−x |
=f′(x0)+3
lim |
x→0 |
f(x0−3x)−f(x0) |
−3x |
=f′(x0)+3f′(x0)=4f′(x0),
故选D.
lim |
x→0 |
f(x0+x)−f(x0−3x) |
x |
lim |
x→0 |
f(x0+x)−f(x0) |
x |
lim |
x→0 |
f(x0+x)−f(x0−3x) |
x |
lim |
x→0 |
f(x0+x)−f(x0)+f(x0)−f(x0−3) |
x |
lim |
x→0 |
f(x0+x)−f(x0) |
x |
lim |
x→0 |
f(x0−3x)−f(x0) |
−x |
lim |
x→0 |
f(x0−3x)−f(x0) |
−3x |