How does one go about evaluating the limits of nonelementary antiderivatives of functions?We obviously know the following to be equal: lim z → ± ∞ erf ( z ) = ± 1But as far as I'm aware, the only way we know how to calculate any given value of the error function is to approximate it. How do we know the limits at infinities without any way to evaluate it algabraically?

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How does one go about evaluating the limits of nonelementary antiderivatives of functions?We obviously know the following to be equal:      lim          z      →      ±      ∞        erf  (  z  )  =  ±  1But as far as I&#039;m aware, the only way we know how to calculate any given value of the error function is to approximate it. How do we know the limits at infinities without any way to evaluate it algabraically?

marktje28 · Accepted Answer

Step 1      lim          x      →      ±      ∞        erf  (  x  )  =      lim          x      →      ±      ∞            2          π            ∫    0    x        e          −              t        2              d  t  =      2          π            ∫    0          ±      ∞            e          −              t        2            using the fact       e          −              t        2             is an even function:  ±      2          π            ∫    0    ∞        e          −              t        2            Step 2The integral is known as the gaussian integral(half of it) and is known to equal             π        2   and thus,      lim          z      →      ±      ∞        erf  (  z  )  =  ±  1

How does one go about evaluating the limits of nonelementary antiderivatives of functions? We obvio

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