Which rule or method can be applied against lim x → 0 1 + 6 x − ( 1 + 3 x ) x 2 ? ?

Question

Which rule or method can be applied against          lim          x      →      0                          1        +        6        x            −              (        1        +        3        x        )                    x              2                 ? ?

Karla Hull · Accepted Answer

L  =      lim          x      →      0                          1        +        6        x            −              (        1        +        3        x        )                    x              2              =      lim          x      →      0                  (              1        +        6        x            −              (        1        +        3        x        )            )              x              2                        (              1        +        6        x            +              (        1        +        3        x        )            )              (              1        +        6        x            +              (        1        +        3        x        )            )        =      lim          x      →      0                          (        1        +        6        x        )            −                        (          1          +          3          x          )                          2                                    x                  2                            (                  1          +          6          x                +                  (          1          +          3          x          )                )              =      lim          x      →      0                  1      +      6      x      −              (        1        +        6        x        +        9                  x                      2                          )                            x                  2                            (                  1          +          6          x                +                  (          1          +          3          x          )                )              =      lim          x      →      0                  1      +      6      x      −      1      −      6      x      −      9              x                  2                                    x                  2                            (        1        +        3        x        +                  1          +          6          x                )              =      lim          x      →      0                  −      9              x                  2                                    x                  2                            (        1        +        3        x        +                  1          +          6          x                )              =      lim          x      →      0                  −      9              (      1      +      3      x      +              1        +        6        x            )        =      lim          x      →      0                  −      9              (      1      +      1      )        =  −      9    2

auto23652im · Accepted Answer

From your line 4:      lim          x      →      0                          3                  1          +          6          x                    −      3              2      x        →            0      0      So by L&#039;Hopital&#039;s Rule,      lim          x      →      0                          3                  1          +          6          x                    −      3              2      x        =      lim          x      →      0                  −              3                  2          (          1          +          6          x                      )                          3                              /                            2                                          ⋅      6        2    =                                          −            3                                2            ⋅            (            1            +            6            (            0            )                          )                              3                                  /                                2                                                    ⋅        6            2        =  −            9      2

Which rule or method can be applied against <mtext> </mtext> <munder> <mo movablelimit

Answered question

Answer & Explanation

New Questions in Differential Calculus