how to check differentiablity of |log|x||

im not able to solve its limits.

You really need to define the domain of the function. Can we assume it is [math]\mathbb{R}[/math], or is it just some subset of this?

 

You need to ask is [math]f(x) = |\log |x||[/math] continuous for all points in the domain?

 

Let [math]I,D \subset \mathbb{R}[/math]. The function [math]f: I \rightarrow D[/math] is continuous at [math]c \in I[/math] if for all [math]\epsilon > 0[/math] there exists [math]\delta >0[/math] such that for all [math] x \in I[/math]

 

[math]|x-c| < \delta[/math] implies [math]|f(x)- f©| < \epsilon[/math].

 

My advice is to plot the function and get a "feel" of what it looks like. Then use the epsilon-delta construction above to see if it is continuous at all points. My intuition tells me to look at the point [math]c = 0[/math].

 

Hope that is of some help.

its coming continuous at c=o.

 

but not at +-1