Limit cos ( pi x /2) / 1-x as x-->1

Answers (1)

Solution:    

              lim_x	o 1fraccos (fracpi x2)1-x

   Let   us put    1-x=z  Then   x=1-z  and   z
ightarrow 0  as  x
ightarrow 1

  Hence .

             lim_x	o 1fraccos fracpi2x1-x=lim_z	o 0 fraccos (fracpi2-fracpi2z)z\ \ Rightarrow hspace0.5cmlim_z	o 0fracsin fracpi2zz=fracpi2.

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