Polynomial Approximation of the Exponential Function

The graph shows plots of (dashed line) and for various values of . It is interesting that for positive values of , the latter expression is a polynomial that converges from below to (the blue and violet lines are the polynomials). For negative values of , the expression is the reciprocal of a polynomial that converges to from above (the green, yellow, and orange curves are the reciprocals of polynomials).