12.1 Exponential and Log Functions

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The following two plots illustrate how two different formulas for $e^{-y}$ exhibit different convergence patterns to the reference function (dashed-gray curve) for $y>0$ as evaluation limits are successively increased (green, orange, and blue curves).

$e^{-y}$
$e^{-y}$

The following plot illustrates a formula for $\log(y)$ converges (albeit rather slowly) to the reference function (dashed-gray curve) for $y>1$ as evaluation limits are successively increased (green,orange, and blue curves).

$\log(y)$