Limit question (1 Viewer)

[Drsoccerball]

 

[seanieg89]

It's a removable discontinuity.

That expression is 0/0 at x=2, which you cannot make sense of (so 2 is not even in the domain of the function defined by that expression). However defining f(2)=-1/3 gives you a smooth function on R \ {5}.

 

[Drsoccerball]

It's a removable discontinuity.

That expression is 0/0 at x=2, which you cannot make sense of (so 2 is not even in the domain of the function defined by that expression). However defining f(2)=-1/3 gives you a smooth function on R \ {5}.

So if the question asked if it was "differentiable at x = 2" would you say yes or no ?

 

[seanieg89]

So if the question asked if it was "differentiable at x = 2" would you say yes or no ?

"No", if I had to say something but neither is really correct because the yes or no question is not a precise mathematical proposition.

It's a silly question because it does not make sense to ask if a function f is differentiable/continuous at a point p outside its domain. A more sensible question is whether or not f has a continuous or differentiable extension to a larger domain containing p, (as this function does).

But this question is logically the same as asking:

Is the function f(x)=x^2 (with domain the real numbers) differentiable at x="apple"?