chitrangda Posted August 29, 2008 Share Posted August 29, 2008 how to check differentiablity of |log|x|| im not able to solve its limits. Link to comment Share on other sites More sharing options...
ajb Posted August 29, 2008 Share Posted August 29, 2008 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. Link to comment Share on other sites More sharing options...
chitrangda Posted August 30, 2008 Author Share Posted August 30, 2008 its coming continuous at c=o. but not at +-1 Link to comment Share on other sites More sharing options...
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