For f ( t ) = ( e t t , 4 t + 1 t ) what is the distance between f(2) and f(5)?

Question

For             f              (        t        )              =          (                        e          t                t            ,      4      t      +              1        t            )       what is the distance between f(2) and f(5)?

gutinyalk · Accepted Answer

Step 1We will substitute first 2 and then 5:            f              (        2        )              =          (                        e          2                2            ,      4      ⋅      2      +              1        2            )        =          (                        e          2                2            ,              17        2            )                  f              (        5        )              =          (                        e          5                5            ,      4      ⋅      5      +              1        5            )        =          (                        e          5                5            ,              101        5            )      Step 2Then we will apply the distance formula:      d    =                                        (                          x              2                        -                          x              1                        )                    2                +                              (                          y              2                        -                          y              1                        )                    2                          d    =                                        (                                          e                5                            5                        -                                          e                2                            2                        )                    2                +                              (                          101              5                        -                          17              2                        )                    2                          =                                        (                                          2                                  e                  5                                -                5                                  e                  2                                            10                        )                    2                +                              (                                          101                ⋅                2                -                17                ⋅                5                            10                        )                    2                          =                                        4                          e              10                        -            20                          e              7                        +            25                          e              4                                100                +                              202            -            85                    100                          =                            4                      e            10                    -          20                      e            7                    +          25                      e            4                    +          117                    10

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