How to solve following limit I've been struggeling a bit with the following limit: lim x → 0 a − a 2 − x 2 x 2 The solution is:If a &lt; 0 then ∞. If a &gt; 0 then 1 2 a But I don't know how to get there.Thank you

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How to solve following limit I&#039;ve been struggeling a bit with the following limit:      lim          x      →      0                  a      −                        a          2                −                  x          2                            x      2      The solution is:If a &amp;lt; 0 then   ∞. If a &amp;gt; 0 then       1          2      a      But I don&#039;t know how to get there.Thank you

potamanixv · Accepted Answer

lim                      x            →            0                                                a            −                                          a                2                            −                              x                2                                                          x            2                                              =                  lim                      x            →            0                                                a            −                                          a                2                            −                              x                2                                                          x            2                          ⋅                              a            +                                          a                2                            −                              x                2                                                          a            +                                          a                2                            −                              x                2                                                                                      =                  lim                      x            →            0                                                x            2                                              x              2                                      (              a              +                                                a                  2                                −                                  x                  2                                            )                                                                        =                  lim                      x            →            0                                    1                      a            +                                          a                2                            −                              x                2                                                                                      =                  1                      a            +                                          a                2                                                        Now the tricky part is how you simplify             a      2       base on the sign of a.

tripes3h · Accepted Answer

We have that      lim          x      →      0                  a      −                        a          2                −                  x          2                            x      2        =      lim          x      →      0                          a        2            −              a        2            +              x        2                            x        2            (      a      +                        a          2                −                  x          2                    )        =      1          a      +              |            a              |            from here you can do

How to solve following limit I've been struggeling a bit with the following limit: <munder>

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