I seek your help on this question. lim x → ∞ ( 9 x 6 + 7 x 3 + 5 x − 9 x 6 + 6 x 2 + 3 x )

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I seek your help on this question.      lim          x      →      ∞            (          9              x        6            +      7              x        3            +      5      x        −          9              x        6            +      6              x        2            +      3      x        )

pheniankang · Accepted Answer

We know that, by asymptotic relations:  (  1  +  f  (  x  )      )          α            ∼      α  ⋅  f  (  x  )      when      f  (  x  )  →  0One can write:      lim          x      →      ∞            (          9              x        6            +      7              x        3            +      5      x        −          9              x        6            +      6              x        2            +      3      x        )    =      lim          x      →      ∞            9          x      6        +    6          x      2        +    3    x    ⋅      (                            9                      x            6                    +          7                      x            3                    +          5          x                          9                      x            6                    +          6                      x            2                    +          3          x                      −    1    )    =      lim          x      →      ∞            9          x      6        +    6          x      2        +    3    x    ⋅      (                            9                      x            6                    +          6                      x            2                    +          3          x          +          (          7                      x            3                    −          6                      x            2                    )                          9                      x            6                    +          6                      x            2                    +          3          x                      −    1    )    =      lim          x      →      ∞            9          x      6        +    6          x      2        +    3    x    ⋅      (          1      +                        7                      x            3                    −          6                      x            2                                    9                      x            6                    +          6                      x            2                    +          3          x                      −    1    )        ∼          lim          x      →      ∞        3      x    3    ⋅      (          1      +                        7                      x            3                                    9                      x            6                                −    1    )            lim          x      →      ∞        3      x    3    ⋅      1    2    ⋅      7          9              x        3              =      7    6  So, the limit is       7    6

I seek your help on this question. <munder> <mo movablelimits="true" form="prefix">lim <

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New Questions in Calculus 1