Taylor and MacLaurin Series: Consider the approximation of the exponential by its third degree Taylor Polynomial:
$e^x \approx P_3(x) = 1+ x + \frac{x^2}{2} + \frac{x^3} {6}.$
Compute the error $e^x-P_3(x)$ for various values of $x$:
$e^0-P_3(0)$ = .
$e^{0.1}-P_3(0.1)$ = .
$e^{0.5}-P_3(0.5)$ = .
$e^1-P_3(1)$ = .
$e^2-P_3(2)$ = .
$e^{-1}-P_3(-1)$ = .