Evaluate Limit ( 1 / x^2 - 1/ sin ^2 x ) As x-->0

Answers (1)

Solution:   

                lim _x	o 0(frac1x^2-frac1sin^2x)=lim_x	o0fracsin^2x-x^2x^2sin^2x

        Rightarrow                                   =      lim_x	o0fracsin^2x-x^2x^4(fracxsin x)^2

         ecause               lim_x	o0(fracxsin x)=1

         Rightarrow                                 =lim_x	o0fracsin^2x-x^2x^4       Form frac00.

        Rightarrow                                  =lim_x	o0fracsin 2x-2x4x^3     Form   frac00

        Rightarrow                                 =lim_x	o0fraccos 2x-16x^2=lim_x	o0[-frac13(fracsin xx)^2]=-frac13.

 

                                          

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