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The Limit of log ( 1- x) / cos pi x As x --> 1

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Solution:  We have , 

                   lim_x o1fraclog (1-x)cot (pi x)  

             Form  fracinfty infty .   Using L'Hospital Rule

     Rightarrow          lim _x o1fraclog(1-x)cot(pi x)=lim_x o 1frac-frac11-x-pi csc ^2pi x

   Rightarrow                                          =lim_x o 1fracsin^2(pi x)pi (1-x)       Form  frac00 

   Rightarrow                                        =lim_x o1fracpi sin (2pi x)-pi=0

 

 

 

Posted by

Deependra Verma

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