Question

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Answer 1

Verified answer

No 3
             1 - (x - 1)¹/²               -1/2(x - 1)⁻¹/²
   lim   ------------------  =  lim   ------------------
 ×→₂        x² - 2x            ˣ→²       2x - 2

                                        - 1/2 (2 - 1)⁻¹/²
                                   = ------------------------
                                            2(2) - 2
                                  
                                           - 1/2
                                   = --------------
                                             2
                                   = - 1/2 x 1/2
                                   = - 1/4
no 4
          3 - (2x + 3)¹/²                - 1/2. 2(2x + 3)⁻¹/²
lim   --------------------   =  lim   ---------------------------
ₓ→₃         x² - 9               ₓ→₃              2x

                                        - 1 (2(3) + 3)⁻¹/²
                                   = ----------------------------
                                                 2(3)

                                          9⁻¹/²
                                   = ------------
                                           6
                                         (3²)⁻¹/²
                                   = -------------
                                            6
                                   =   1/3 x 1/6
                                   =   1/18