CPM Homework Help : CALC Problem 12-66

Find the fourth-degree Maclaurin polynomial for $f(x) = e^{−2x}$ . Use it to approximate $f ( 0.5 ) = e ^ { - 1 } = \frac { 1 } { e }$ , and find a bound for the error in this approximation. Then approximate $f^{\prime\prime\prime}(0.5)$ .

Hint:

The Maclaurin series for $e^{x}$ is:
Substitute $–2x$ for $x$ to get the polynomial for $e^{–2x}$ .
To bound the error, determine the $x^{5}$ term in the polynomial and evaluate it for $x = 0.5$ .