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Unit 7: Limits




                                                                                                Notes
               or

               Thus,



          (iv)  Prove that

          Proof: By Binomial theorem, when |x|<1, we get









                                 =

                                 =


                                 =


                                 =  e (By definition)

                 Thus


          (v)  Prove that
                                 =


                                 =  log e


                                 =  1

          (vi)  Prove that


          Proof: We know that

                              e  =


                            x
                           e  – 1  =


                                 =




                                 =





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