Argue that lim g(x), with x → -1, = -2

[SixBooks]

Hello, everybody!

The function g: R → R is differentiable in -1, g' (-1) = 2 and g (-1) = -2. Can someone show me (how to argue) that lim g(x), with x → -1, = -2?

Thanks in advance!

 

[STEMucator]

If a function is differentiable at a point, then it is continuous there.

If $g$ is differentiable, then:

$$\displaystyle \lim_{x -> a} \frac{f(x) - f(a)}{x - a} = f'(a)$$