Find lim x → ∞ ( x 2 + 1 x 2 − 1 ) x 2 How to calculate the following limit?

Question

Find        lim          x      →      ∞                  (                                    x            2                    +          1                                      x            2                    −          1                    )                      x        2            How to calculate the following limit?

Charlize Manning · Accepted Answer

lim          x      →      ∞                  (                          x        2            +      1                      x        2            −      1                          )                            x        2              =      lim          x      →      ∞                  (        1  +      2                  x        2            −      1                          )                                                  x            2                    −          1                2            ⋅                        2                      x            2                                                x            2                    −          1                      =      e                  lim                  x          →          ∞                                      2                      x            2                                                x            2                    −          1                      =      e    2

fythynwyrk0 · Accepted Answer

it&#039;s the same as that of            (                        1          +          1                      /                    n                          1          −          1                      /                    n                    )              n      Without the bottom, this gives e as is well known.  (  1  −  1      /    n      )          −      1        =  1  +  1      /    n  +  1      /        n    2    +  .  .  .multiplying we get  (  1  +  2      /    n  +  O  (      n          −      2        )      )    n  If we drop the   O term we get       e    2    .it simply remains to show that the final error disappears in the limit.

Find <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXAtom-ORD

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