Defining priority of operations in limits with stacking fractionsI need to evaluate the following limit : lim x → ∞ ln ⁡ ( x 2 + 1 ) x 2 Using L'Hospital rule, I get this result (which I'm pretty sure is good) lim x → ∞ 2 x x 2 + 1 2 x Now, I'm not sure how I must evaluate this. Either as : lim x → ∞ 2 x x 2 + 1 ∗ 1 2 x = 1 x 2 + 1 or lim x → ∞ 2 x ∗ ( x 2 + 1 2 x ) − 1 = 4 x 2 x 2 + 1 According to most of the tools I use to validate my maths, the 1st result is the good one, but I can't figure out why, am I simply missing a set of parenthesis in my equation?

Question

Defining priority of operations in limits with stacking fractionsI need to evaluate the following limit :      lim          x      →      ∞                  ln      ⁡      (              x        2            +      1      )              x      2      Using L&#039;Hospital rule, I get this result (which I&#039;m pretty sure is good)      lim          x      →      ∞                          2        x                              x          2                +        1                    2      x      Now, I&#039;m not sure how I must evaluate this. Either as :      lim          x      →      ∞                  2      x                      x        2            +      1        ∗      1          2      x        =      1                  x        2            +      1      or      lim          x      →      ∞        2  x  ∗  (                    x        2            +      1              2      x            )          −      1        =            4              x        2                            x        2            +      1      According to most of the tools I use to validate my maths, the 1st result is the good one, but I can&#039;t figure out why, am I simply missing a set of parenthesis in my equation?

Tianna Deleon · Accepted Answer

This is just elementary algebra:                              a          b                    c        =            a              b        ⋅        c            i.e.,   a      /    b divided by   c equals   a divided by   b  c. Thus, the first result which you have obtained is the correct one. In the second equation, you wrote  2  x  ⋅            (                                    x            2                    +          1                          2          x                    )              −      1      instead of the correct            1              2        x              ⋅            (                                    x            2                    +          1                          2          x                    )              −      1

Defining priority of operations in limits with stacking fractions I need to evaluate the following

Answered question

Answer & Explanation

New Questions in Pre-Algebra