Continuity and L’Hospital’s Rule

March 22, 2008

Consider the function

f(x) =\Biggl\{ \begin{array}{lcl} \cos x, & \mathrm{if} & x=0,\\ \displaystyle x \ln x (1-x) ^{-1}, & \mathrm{if} & 0<x<1, \\ -1, & \mathrm{if} & x=1. \end{array}

Discuss the continuity of f on \left[0,1\right].

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