What is the continuity of f ( t ) = 3 - 9 - t 2

Question

What is the continuity of             f              (        t        )              =    3    -                  9        -                  t          2

Warkallent8 · Accepted Answer

f              (        t        )              =    3    -                  9        -                  t          2                     has domain             [      -      3      ,      3      ]      For a in             (      -      3      ,      3      )      ,             lim              t        →        a                    f              (        t        )              =          f              (        a        )             because            lim              t        →        a                    (      3      -                        9          -                      t            2                              )        =    3    -          lim              t        →        a                            9        -                  t          2                          =    3    -                            lim                      t            →            a                                    (          9          -                      t            2                    )                      =    3    -                  9        -                  lim                      t            →            a                                    t          2                      )        =    3    -                  9        -                  a          2                      =          f              (        a        )            So f is continuous on (−3,3).Similar reasoning will show that            lim              t        →        -                  3          +                            f              (        t        )              =          f              (        -        3        )             and            lim              t        →                  3          -                            f              (        t        )              =          f              (        3        )            So f is continuous on [−3,3].

What is the continuity of f(t) = 3 - sqrt(9-t^2)

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